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284 Cards in this Set
- Front
- Back
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Capital allocation Line (CAL)
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A line that shows the relationship between risk (sigma) and return (expected return minus risk-free rate).
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Sharpe ratio
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Also called the "reward to volatility" ratio. (Expected return minus risk free return) / (sigma)
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Optimal portfolio
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Has maximum utility. Optimal ratio given by y* = [E(r) - rf]/
(A * sigma^2) |
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Indifference curves
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Contain portfolios that investors are indifferent about.
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Active vs. Passive
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Active: determined with security analysis
Passive: benchmark portfolio selected; analysis is unecessary |
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Advantages of passive approach to investment
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-Cheaper than active
-Free-rider benefit: can benefit from the already fairly-priced market |
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What is the relevance of the intersection of the CAL and the indifference curve?
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This intersection determines the optimal portfolio.
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3 levels of risk appetites
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1. Risk averse
2. Risk neutral 3. Risk lovers |
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Define the "Complete portfolio"
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The entire portfolio of the investor, made up of risk free assets and risky assets.
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Portfolio A dominates Portfolio B if:
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E[r_a] > R[r_b] AND
sigma _a <= sigma_b |
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Equation for the CAL (capital allocation line)
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E[r_c] = r_f + (sigma_c)/(sigma_p) * [E[r_p] - r_f]
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Describe the "Capital Market Line"
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Capital allocation line that uses the market portfolio as the risky asset.
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Total variance (risk) of a portfolio of equally weighted assets
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variance = (mean variance)/n + [(n-1)/n]*Cov
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2 categories of risk
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1. Market/systematic/nondiversifiable risk: cannot be diversified away.
2. Unique/firm-specific/nonsystematic/diversifiable: portion of the risk that can be eliminated via diversification |
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Describe "Efficient Diversification"
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A portfolio with the lowest risk for a given return.
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Explain the Separation Principle
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There are 2 steps to portfolio selection:
1) Selection of optimal risky portfolio. 2) Allocation between risk free vs. risky assets. |
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2 problems with the Markowitz model
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1. As the number of securities increases, the number of variables that need to be calculated increases dramatically.
2) Due to the large number of required estimates, it is likely that some variables are estimated incorrectly. |
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Describe the "single index model."
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Version of the single-factor model, where the return on an index is used as a proxy for the common factor.
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Variance and covariance of a security in the single-factor model.
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sigma_i^2 = beta^2*sigma_m^2 + sigma_i^2
Cov(r_i,r_j) = beta_i*beta_j * sigma_m^2 |
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Advantage of single index model:
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Significantly fewer estimates are needed than the number needed for the Markowitz model.
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Equation of the single index model
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E(R_i) = alpha_i + beta_i * E(R_m)
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Disadvantage of the single index model
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Oversimplifies the true uncertainty.
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Equation for firm-specific risk (assuming a portfolio of equally weighted securities)
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sigma(e_p)^2 = (1/n)*sigma(e)^2
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CAPM assumptions
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-There are many investors, who are all price-takers
-Investors plan for one holding period -Investors are limited to publicly traded financial assets -Investors can borrow or lend at the risk-free rate -There are no taxes or transaction costs -All investors are rational mean-variance optimizers -Investors have homogeneous expectations |
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Implications of CAPM assumptions
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-All investors will hold the market portfolio, M.
-The CML is the best attainable capital allocation line -The risk premium on the market portfolio is proportional to its risk and degree of risk aversion -The risk premium on individual assets is proportional to the risk premium on M and beta |
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Equation for the price of market risk
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[E(r_M)-r_f]/sigma_m^2
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Equation for CAPM
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E(r_i) = r_f + beta_i * [E(r_M) - r_f]
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Difference between CML and SML
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CML: graphs risk premium of efficient portfolios as a function of sigma
SML: graphs risk premium of individual assets as a function of beta |
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2 examples of non-traded assets
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1. Human capital
2. Privately held businesses |
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Describe the Impact of CAPM from privately held businesses that have similar characteristics to traded assets
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Little impact: owners of these businesses can still achieve diversification by holding similar traded assets.
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Impact of CAPM from privately held businesses that do not have similar characteristics to traded assets
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Owners of these businesses will bid up the prices of hedge assets, reducing their expected return. They will appear to have a negative alpha.
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Impact to CAPM from human capital asset
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Since employees will avoid purchasing shares of their own employer, the shares of labor intensive firms will have lower demand, and therefore appear to have a positive alpha.
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Describe an "Arbitrage Opportunity"
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The opportunity to make a riskless profit without the need to make a net investment.
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2 requirements of the factors chosen to be used in factor models/APT models
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1. Should have considerable ability to explain security returns.
2. should be important risk factors. |
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Describe the "Law of One Price"
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Two assets that are equivalent in all economically relevant aspects should have the same market price.
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3 assumptions of the APT
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1. Security returns can be described by a factor model.
2. There are a sufficient number of securities to diversify away idiosyncratic risk. 3. Well functioning securities markets do not allow for the persistence of arbitrage opportunities. |
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Advantage of APT over CAPM
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Lower reliance on assumptions in derivation.
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Advantage of CAPM over APT
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CAPM applies to all securities (no exceptions)
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What does the Efficient Market Hypothesis (EMH) state?
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Stock prices should reflect all available information.
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Briefly describe 3 versions of the EMH
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1. Weak form: stock prices reflect all information that can be derived from existing market data.
2. Semistrong form: stock prices reflect all publicly available information about the firm's prospects 3. Strong form: stock prices reflect all information relevant to the firm, including that not publicly available. |
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Describe "Technical Analysis"
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Technical Analysis is the search for predictable patterns of stock prices, which can be used to derive a profit from trading.
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Describe "Fundamental Analysis"
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Uses the fundamentals of a firm to determine the appropriate price.
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2 difficulties with conducting "event studies," and how to deal with each.
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1. the stock price may respond to a wide range of economic news in addition to the specific event: base the impact on the abnormal returns.
2. information about the event may be leaked prior to the actual event: measure the "cumulative abnormal return," starting at a point in time prior to the event. |
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3 resons why it is difficult to determine if the markets are truly efficient
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1. Magnitude Issue: the impact of the investment manager may be very small compared to the normal volatility of the market.
2. Selection Bias Issue: once an investment scheme becomes known to others, it will no longer generate abnormal returns. 3. Lucky Event Issue: the number of investors is so large, just by chance, some have to make huge returns. |
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Examples of weak-form tests of EHM
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Returns over short horizons: look at whether investors can use historic trends to earn abnormal profits over the short term, by measuring the serial correlation of stock market returns
Returns over long horizons: similar to the prior test, but looks at the long term returns. |
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Describe semistrong tests of EMH
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Investigate whether publicly available information beyond the trading history can be used to generate abnormal returns.
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Examples of efficient market anomalies
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-Small firm in January effect: small firms have historically generated superior returns, particularly in January
-Book-to-Market Ratios: High Book-to-Market firms have historically outperformed the rest of the market. -Post-Earnings Announcement price drift: the cumulative abnormal returns of stocks has been shown to continue to increase even after the information about the event becomes public |
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2 reasons efficient market anomolies are not necessarily a sign that the market is efficient
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1. the properties are proxies for fundamental determinants of risk.
2. the properties arise just due to data mining. |
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Three uses of portfolio management, even if markets are efficient
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1. Diversification
2. Tax considerations 3. Adjusts porfolio to reflect individual investor's risk appetite. |
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Briefly describe 2 categories of irrationalities
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1. Investors do not always process information correctly, and therefore derive incorrect probability distributions.
2. Investors often make inconsistent/suboptimal decisions due to their behavioral biases. |
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4 biases that cause information processing errors
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1. Forecasting Errors: too much weight is assigned to recent experience/forecasts are too extreme given the actual level of uncertainty.
2. Overconfidence: many investors overestimate their abilities. 3. Conservatism: Investors are too slow to update their beliefs in response to new evidence. 4. Sample Size Neglect & Representativeness: Investors do not account for sample size, and therefore may infer a pattern based on too small a sample. |
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Examples of behavioral biases
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-Framing: Decisions are often materially impacted by how the question is framed.
-Mental Accounting: Investors may segregate decisions. Rationally, it would be better to optimize the risk-return profile for the entire portfolio in aggregate. -Regret Avoidance: Investors who make decisions that turn out badly have more regret if it were an unconventional decision. -Prospect Theory: This modifies the standard financial theories' definition of risk averse investors. |
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List 2 examples where the Law of One Price has been violated.
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1. Siamese Twin Companies.
2. Equity Carve-outs |
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List 3 criticisms of Behavioral Finance
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1. The behavioral approach is too unstructured: it allows virtually any anomaly to be explained by a combination of irrationalities.
2. Some anomalies are inconsistent in their support for one irrationality vs another. 3. Selecting the wrong benchmark can produce an apparent abnormality. |
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Factors that limit the actions of arbitrageurs
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-Fundamental risk: Their actions are actually not risk free, because the mispricings are not necessarily going to disappear.
-Implementation Costs: Arbitrageurs usually need to rely on short selling in order to exploit overpricing. There are often limitations to short selling. Model risk: It is possible that the prices are indeed valid. Instead, there may be issues with the arbitrageurs model that are causing it to falsely indicate a mispricing. |
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Describe 3 approaches that try to profit from trends.
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1. Dow Theory: based on the predictability of trends: there is a long term movement upwards, and any deviations are eventually corrected.
2. Moving Averages: If the market breaks through the moving average line from below, this is a bullish signal, as it is a sign of a shift from a falling trend to a rising trend. 3. Breadth: This measures how widely the movement in the market index is reflected in the price movements of all stocks. |
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List 3 diagnostics used by technical analysts to measure market sentiment
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1. Trin Statistic
2. Confidence Index 3. Put/Call ratio |
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Equation for the "Trin Statistic"
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Trin = [(Volume declining)/(Number Declining)] / [(Volume advancing) / (Number advancing)]
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Equation for the "confidence Index"
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Confidence Index = (Avg yield on top 10 rated corporate bonds) / (Avg Yield on intermediate 10 rated corporate bonds)
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Describe the "unconditional default probability"
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The probability that a bond that exists at time zero will default during a given future period.
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Describe the "default intensity"
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The probability that a bond will default during a future period, given that it has not defaulted as of the start of the period.
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Equation for the probability of defaulting by time t
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Q(t) = 1 - exp(lambda(t)*t)
Where lambda(t) is the average default intensity between zero and time t. |
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Equation to calculate the probability of default using bond prices and the "simple method."
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lambda(t) = s/(1-R)
Where s is the spread between the yield of a bond and an equivalent risk-free bond. |
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Probability of default using the Black-Scholes model
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N(-d2)
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Additional equation needed to calculate V0 and sigma_v (derived with Ito's lemma)
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sigma_E * E_0 = N(d_1*sigma_v * V_0)
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Equation to calculate the credit risk adjusted value of a derivative, based on data from bonds issued by the derivative issuer.
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f_0* = f_0 * exp(-(y*-y)*T)
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3 clauses of derivatives contracts to reduce credit risk exposure.
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1. Netting: if a company defaults on one contract with a counterparty, it must default on all outstanding contracts.
2. Collateralization: contracts need to be revalued periodically, and collateral needs to be posted to make up for any deficiencies from a threshold value 3. Downgrade Triggers: if the credit rating of the counterparty falls below a specific level, the financial institution has the option to close out the contracts. |
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Limitation of a collateralization clause
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If the company does get into financial difficulties, it will most probably stop responding to requests to post collateral.
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2 limitations of the downgrade triggers clause
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1. Provides little protection against a large ratings jump
2. only works well if counterparty only has issued a few contracts with downgrade triggers |
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List 2 reasons that default rates by different companies are often correlated.
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1. companies in the same industry / geographic region are affected by similar economic events.
2. a default by one company may cause a default by another |
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2 advantages of credit metrics
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1. Accounts for the impact of credit downgrades rather than just defaults
2. Can incorporate credit migration clauses. |
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1 disadvantage of credit metrics
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computationally time intensive.
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Briefly describe the structure of a credit default swap
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-The buyer makes CDS spread payments to the seller until maturity
-If a credit event occurs, the buyer has the right to sell bonds for their face value (notional principal) to the seller |
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Briefly describe the 2 possible forms of settlement of a CDS payment
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1. physical settlement: the protection buyer can sell the bonds to the protection seller at face value
2. cash settlement: the seller will make a payment to the buyer, which is based on the difference between the face value and the value of the "cheapest deliverable bond" |
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What is a "collateralized debt obligation?"
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An ABS where the pool of assets consists of bonds issued by corporations or countries.
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How is a "synthetic CDO" created?
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Created from the short positions in CDS: default losses are allocated to tranches
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Why does systematic risk make up such a large portion of the overall risk of structured products?
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Because structured products pool together the risk from several assets, the non-systematic risk is usually diversified away
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List 3 examples of the deteriorating quality of mortgages in the last decade.
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1. Ratio of mortgage values to home prices increased
2. Increased use of second lien loans 3. Increased issuance of mortgages with low/no documentation. |
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List 4 characteristics of CMOs that are biased against investors
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1. Higher probability of default due to lower credit quality of borrowers.
2. Lower recovery values, because when the assets do need to be sold, they are often sold under financial pressure. 3. High level of default correlation due to pooling mortgages from similar geographic areas/vintages. 4. Due to the CDO2 structure, the impact of errors in the estimates is magnified. |
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Define liquidity
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The ability to meet expected and unexpected demands for cash, while suffering minimal losses.
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List examples of events that may cause liquidity problems
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-credit rating downgrade
-negative publicity -deterioration of economy -news of problems of other companies in similar lines of business |
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Examples of company specific factors that will magnify liquidity risk
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-A small group of agents/brokers control large portions of the business
-The size of the company -subject to immediate demands on cash -unpredictable deferrable demands on cash -insufficient ability to borrow short term -lack of diversity of liabilities/ assets |
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Briefly describe the 3 levels of liquidity risk management
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-day to day cash management: focuses on daily cash flow volatility
-Ongoing/intermediate term cash flow management: focuses on the next 6 - 24 months -Stress liquidity risk management: focuses on catastrophic risk. Examines the ability of the company to meet several cash demands simultaneously. |
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Briefly describe the steps of the stress liquidity management process.
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1) Product design/portfolio strategy: involves matching the portfolio management strategy with the product features.
2) monitoring: both the current and projected positions need to be monitored. 3. Preparedness to act: if the liquidity risk does become a problem, the management needs to use the available tools to reduce the risk. |
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List sources of liquidity that may be available in a stress scenario
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-Asset sales
-Asset securitizations: this involves selling a pool of assets as a security -borrowing -selling additional business |
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Tools available to help reduce liquidity risk
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-cash flow match
-diversify assets -diversify liabilities -ladder liability maturities -back surplus / capital with liquid assets -establish a durable line of credit -issue commercial paper -use repurchase agreements |
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2 tools available to measure a company's exposure to liquidity risk
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1. Cash flow modeling
2. Liquidity ratios: compare liquidity adjusted assets to liquidity adjusted liabilities. |
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When considering the liquidity risk from currency exposure, list 4 factors that the banks need to consider
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1. the ability to raise funds in foreign currency markets
2. the extent of foreign currency backup facilities available in the domestic market 3. the ability to transfer a liquidity surplus from one currency to another. 4. the likely convertibility of currencies |
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list examples of early warning indicators of impending liquidity problems
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-rapid asset growth
-Growing concentrations in assets or liabilities -increases in currency mismatches -decrease of weighted average maturity of liabilities -significant deterioration of earnings -negative publicity -credit rating downgrade -stock price decline |
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List examples of sources of funding to the insurer
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-Deposit growth
-Lengthening of maturities of liabilities -new issues of debt instruments -Intra-group funds transfers -Asset securitization |
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Define "liquidity management"
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Ensuring that there are sufficient assets to meet obligations when they fall due, without having to incur unreasonable costs
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List changes in the banking environment that have resulted in an increase in their exposure to liquidity risk
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-increased use of securitization
-increased use of complex financial instruments -increased use of collateral -introduction of intra day payments -integrated financial markets |
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List examples of challenges of complex financial instruments to the banks in managing their liquidity risk
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-These instruments usually have credit downgrade clauses/call features that make it a lot more difficult to assess their liquidity
-They are not actively traded, so it is difficult to determine their market value -Due to their short history, it is very difficult to predict their cash flows, and correlation with other financial assets during stress scenarios. |
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List some factors that have amplified the liquidity risk to the banks
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-securitization
-complex financial instruments -collateral usage -payment systems -cross border flows |
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List some lessons that banks learned from the 2008 financial crisis
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-stress testing
-contingency funding plans -off-balance sheet activity and contingent commitments -balance sheet management -capital -supervisory and market information -central bank facilities -cross border issues |
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List the 4 great derivative disasters discussed by the authors
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1) P&G
2) Barings 3) Orange County 4) MGRM |
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Briefly describe the P&G disaster
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P&G entered into a fixed for floating interest rate swap, where it made floating interest payments, and received fixed payments. Increases in interest rates caused by P&G to incur $150M of losses
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Briefly describe the Barrings disaster
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Barings Bank failed in 1995 due to the actions of a rogue trader who made bad bets on the Japanese stock market.
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List 2 reasons that the authors believe that the P&G disaster would not have been prevented by carrying out VaR analysis
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1) VaR is not designed to be applied to single transactions
2) P&G was probably more concerned with cash flow risk than value risk, and therefore the management may not necessarily have been monitoring and controlling the VaR. |
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Why do the authors believe that the Barrings disaster would not have been prevented by carrying out VaR analysis
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Management did not even know about the trades because of poor controls: the trader was allowed to record his own trades, and intentionally neglected to disclose several to hide his actions.
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Briefly describe the Orange County disaster
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Orange County made bets on the slope of the yield curve, by purchasing intermediate term securities which they financed with short term borrowing. Interest rates increased, causing the intermediate term securities to depreciate, and the cost of short term borrowing to increase.
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Why do the authors believe that the Orange County disaster would not have been prevented by carrying out VaR analysis?
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The manager of the pool was most probably aware of the risks, but still intentionally make these trades due to potential profits.
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Briefly describe the MGRM disaster
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MGRM offered customers long term price guarantees for gasoline/fuel oil. To hedge these guarantees, MGRM purchased short term futures contracts. Oil prices actually fell for several months, and MGRM had to make several margin calls on its losing futures position.
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Why do the authors believe the MGRM disaster would not have been prevented by carrying out VaR analysis?
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The problem was not the change in value of the portfolio, but rather the change in cash flows. Since VaR analysis focuses exclusively on value, it would not have alerted management to the cash flow problems.
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Briefly describe 2 alternatives to VaR
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1) Cash Flow Risk: useful for companies that are more concerned with the volatility of cash flows than value. Based on a distribution of cash flows.
2) Shortfall risk: rather than determining a dollar loss associated with a given arbitrary probability, it determines a probability associated with a particular given loss (shortfall) |
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3 examples of friction costs
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1) Agency & Informational costs: management may behave opportunistically, and therefore fail to achieve the owner's objective of value maximization
2. Double taxation 3. Regulations may force the insurer to hold inefficient investment portfolios |
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3 reasons that RBC shouldn't be used to allocate capital
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1. The factors used in the derivation of the RBC are of questionable accuracy.
2. The calculations are often based on book value instead of market 3. RBC ignores several important sources of risk. |
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3 reasons VaR shouldn't be used to allocate capital
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1. The firm may not have enough capital to achieve a certain exceedence probability
2. This does not consider the impact of diversification 3. This does not reflect the amount by which losses will exceed the resources in the event that the exceedence level is breached. |
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List examples of risk linked securities
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-CAT bonds
-sidecars -Catastrophic equity puts -Catastrophic risk swaps -Industry loss warranties |
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Briefly describe the 3 types of triggers that would generate a payment from a CAT bond
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1) Indemnity triggers: the payouts are based on the sponsoring insurer's actual losses
2) Index triggers: the payouts are based on an index of industry losses 3) Hybrid triggers: these blend more than one trigger |
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Briefly describe the 3 types of index triggers
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1) Industry loss indices: the estimated losses to the industry from an event
2) model loss indices: runs the parameters of the event through a model of a catastrophe-modeling firm to generate losses 3) parametric indices: triggered by specified physical measures of an event |
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What trade off is made when selecting a trigger?
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Between moral hazard and basis risk
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Who is most concerned about moral hazard? What is the appropriate trigger to protect against this?
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Investors are most concerned. The appropriate trigger is Industry Loss Index.
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Who is most concerned about basis risk? What is the appropriate trigger to protect against this?
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The Sponsor is most concerned about basis risk. The Indemnity trigger is the appropriate trigger to protect against this.
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Disadvantage to insurer of using the Industry Loss index trigger
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Higher basis risk
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List 2 disadvantages to the insurer of using an Indemnity trigger
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1) may need to reveal confidential info
2) May require more time to reach a settlement due to length of loss adjustment process |
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List 2 disadvantages to the investor of using an Indemnity trigger
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1) potential for moral hazard
2) needs to obtain info on the sponsor's portfolio |
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2 reasons the high layers of exposure are often uninsured
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1) The credit risk of the reinsurer is a major concern in events of this magnitude
2) the highest layers usually have the highest reinsurance profit margins |
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List 3 reasons why CAT bonds are superior to reinsurance when insuring the high layers of exposure
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1) CAT bonds are fully collateralized, so credit risk is not a concern.
2) Investors are willing to accept lower spreads from CAT bonds because they offer diversification benefits. 3) multi-year bonds are available, sheltering the sponsor from the cyclical price fluctuations of the reinsurance market |
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Describe a "sidecar"
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SPVs formed by insurers or reinsurers to provide additional capacity to write reinsurance
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2 advantages of a "sidecar" structure
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1) transactions are usually off-balance sheet, and therefore can be used to improve the reinsurance leverage
2) can be formed quickly with minimal documentation/admin costs |
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Briefly describe how a CAT-E-Put works
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The insurer purchases the Put from the writer, and receives the right to issue preferred stock to the writer at a specified price on the occurrence of a specified event.
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2 advantages of a Cat-E-Put
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1) the insurer will be able to raise equity after a catastrophe, when its stock price is likely to be depressed
2) lower transaction costs than CAT bonds, as no need to form an SPR |
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2 disadvantages of a Cat-E-Put
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1) Not collateralized, so exposes the insurer to credit risk
2) if the insurer issues preferred stock, the value of the existing shares will be diluted |
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2 advantages of a Catastrophe risk swap
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1) the reinsurer reduces some of its core risk, and achieves diversification
2) lower transaction costs than some of the other securities |
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3 disadvantages of a catastrophe risk swap
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1) it is difficult to create a swap that achieves parity
2) can create more exposure to basis risk than some other types of contracts 3) not prefunded |
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Briefly describe the dual triggers of an ILW
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retention trigger: based on the incurred loss of the insurer
warranty trigger: based on an industry-wide loss index |
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list 3 factors that could potentially threaten the growth of the risk linked securities market
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1) regulatory issues
2) accounting issues 3) tax issues |
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2 alternative methods of increasing the chance that a CAT bond will receive reinsurance treatment
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1) base the payment on narrowly defined geographic indices
2) dual-trigger contracts (where the insurer can not collect more than its net loss) |
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Equation for RAROC
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RAROC = (Income) / (Risk - Adjusted Capital)
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List 4 alternative measures of income that can be used in the RAROC calculation
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1) GAAP Net Income: calculated using GAAP accounting
2) Statutory Net Income: calculated using statutory accounting rules 3) IASB Fair Value: based on Fair value accounting 4) Economic profit: the change in "economic value" of the firm over a period |
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List 3 problems with the "Economic Profit" measure
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1) Ignores franchise value
2) may make less sense to management, as the economic values often do not reconcile to GAAP accounting 3) management may have difficulty justifying their decisions to external parties, as these parties only have access to statutory and GAAP accounting |
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List 6 alternative measures of capital
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1) Actual committed capital: The actual capital provided by the shareholders.
2) Market value of equity: the market capitalization 3) Regulatory Required Capital 4) Rating agency required capital: the amount of capital necessary to achieve a specified credit rating 5) Economic capital: the amount of capital necessary to provide teh firm with a certain probability of achieving a specified objective over the time horizon 6) Risk Capital: the amount of capital that needs to be provided by the shareholders to cover the risk that the liabilities may exceed the funds already provided. |
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2 different objectives that can be used to derive the amount of economic capital
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1) Solvency Objective: that the firm can meet its existing obligations to policyholders
2) Capital adequacy objective: that the firm can continue to pay dividends/grow premiums/maintain a certain financial strength |
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3 ways to derive the thresholds that are used to compare to the risk measures
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1) Bond default probabilities at a Selected Credit Rating Level: maintain enough capital that would result in a probability of default of the firm equal to the probability of default of a bond with a specified credit rating
2) management risk preferences: a threshold based on the risk tolerance of management 3) Arbitrary default probability: an arbitrary percentile that is relatively easy to measure. |
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2 disadvantages of using bond default probabilities as a threshold for the risk measure.
|
1) does not address which credit rating should be targeted
2) does not account for the risk downgrade |
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2 disadvantages of using management's risk preferences as a threshold for the risk measure
|
1) will be difficult to get management to articulate and agree on a threshold
2) the preferences of managers will often differ from the preferences of directors and shareholders |
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5 main categories of risk to which an insurer is exposed
|
1) Market risk
2) Credit risk 3) Insurance Underwriting Risk 4) Operational Risk 5) Strategic Risk |
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3 sources of exposure to credit risk to the insurer
|
1) Marketable securities/ derivatives/ swap positions
2) Insureds contingent premiums and deductibles receivable. 3) Reinsurance recoveries |
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3 reasons that the insurers credit risk exposure to reinsurance recoveries is unique
|
1) definition of "default": if the reinsurers credit rating gets downgraded below an investment grade level, it could enter a "death spiral" where its policyholders try to end their contracts, resulting in severe liquidity problems
2) substantial contingent exposure: the reinsurance recoverable at a given point in time may increase in the future due to adverse loss development 3) reinsurance credit risk is highly correlated with the underlying insurance risk |
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2 disadvantages of using Empirical analysis to quantify dependency between risks
|
1) usually there is insufficient data to calculate the historical dependency
2) there is little insight as to how the dependencies will change during tail events |
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3 methods to quantify the dependency between risks
|
1) Empirical Analysis of Historical Data
2) Subjective Estimates 3) Explicit Factor Models: These link the variability of the risks to common factors |
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2 advantages of using subjective estimates to quantify dependency between risks
|
1) can account for tail events
2) reflects the users intuition |
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1 disadvantage of using subjective estimates to quantify dependency between risks
|
As the number of risk categories increases, the number of dependency parameters that need to be estimated increases exponentially
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List 4 techniques to aggregate the distributions of the different risks
|
1) Closed form solutions
2) Approximation methods: eg. assume that all of the individual distributions are normal or lognormal, and then derive the parameters of the aggregate 3) simulation methods 4) square root rule (described in Goldfarb) |
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List the available methods to allocate capital
|
1) Proportional allocation based on risk measure
2) incremental allocation 3) marginal allocation (Myers-Read) 4) co-measures approach |
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3 types of "real" costs to the firm from volatile cash flows
|
1) Higher expected bankruptcy costs: lawyers fees/court fees/interference from court investment and operating decisions/increased difficulty raising funds
2) higher expected payments to stakeholders to compensate for risk 3) higher expected tax payment. |
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Recommend the risk management strategy for a company with very little debt, and almost no chance of default
|
-Since the low end of the tail never reaches the range where it imposes financial distress costs, there is no reason to hedge
-It can also take bets if it has specialized information |
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Recommend the risk management strategy for a company with a lower rating, and with a significant probability of distress
|
-hedge exposures to minimize its probability of default
-don't take bets, nor allow management let their views influence the hedge ratio |
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Recommend the risk management strategy for a company already in distress
|
The firm should not only accept its bets, but also look for additional bets in order to increase the probability of upper tail outcomes
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2 problems calculating VaR over a longer time period
|
1) insufficient data to conduct empirical tests
2) VaR usually relies on the normal distribution, but tail probabilities are usually greater than those implied by the normal distribution. |
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3 problems of using fixed Profit Margin when pricing insurance policies
|
1) Lack of theoretical justification of the fixed profit margin
2) High interest rates suggest the fixed margins may be too low 3) Doesn't reflect increasing competetiveness of the insurance industry |
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List and briefly describe the 2 markets of insurance transactions
|
Financial Market:
-transactions between shareholders and insurer -return to shareholders depends on the risk investment Products Market: -transactions between policyholder and insurer -premium depends on supply/demand of insurance |
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What is the difference between "IRR" and "Opportunity Cost"
|
IRR: rate which sets the NPV of cash flows to zero
Opportunity cost: the investment return that providers of capital could earn from an alternative investment |
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Describe how companies use IRR to decide whether to undertake an investment
|
If IRR > Opportunity cost, project should be profitable
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List 2 assumptions for timing of surplus commitments/ release that an insurer can make
|
1) Surplus is committed once a policy is written, and no longer needed when it expires
2) surplus is committed when UEPR is established, and declines as losses are paid. |
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2 situations when NPV and IRR may give different conclusions
|
1) Projects with unusual cash flows
2) Projects with budget constraints/ mutually exclusive projects |
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Problem of IRR for projects with unusual cash flows
|
If cash flow patterns change between inflow and outflow more than once, there may be two positive roots to the IRR
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Reasons that IRR can be used for expected cash flows, whereas NPV should be used for actual cash flows
|
Expected cash flows do not usually have sign reversals, but actually may.
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Reason that IRR and NPV analyses may give different results for mutually exclusive projects
|
The IRR analysis assumes that the revenues are invested at the IRR, which isn't necessarily true
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2 reasons that insurers reinvestment rate is usually equal to the IRR
|
1) If a pricing model produces an IRR which is greater than the cost of capital, insurers can use this extra revenue to write more policies
2) Policies are usually priced using an underwriting profit provision which sets the IRR equal to the cost of capital. |
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List a practical criticism of the IRR
|
If IRR>0 but less than the Cost of Capital, regulators may get the false impression that the insurer is unprofitable.
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Why are insurers more likely than other companies to have positive IRRs less than the cost of capital
|
Deteriorating results are usually associated with an increase in its reserves. This increase in reserves results in increasing investment income, which offsets poor underwriting results.
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7 risks that surplus is meant to protect against
|
1) Asset risk: chance that assets will depreciate
2) Pricing risk: chance that losses and expenses are ultimately greater than initially expected 3) Reserving risk: risk that reserves are insufficient 4) Asset-liability risk: changes in interest rates will affect the market value of assets differently than liabilities 5) catastrophe risk 6) Reinsurance risk: risk that reinsurance recoverables won't be collected 7) credit risk: risk that agents/insureds won't remit premium |
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When deriving surplus required, some insurers do not distinguish between policy form. Give an example of a type of policy that will therefore have overstated surplus required
|
Retro
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When deriving surplus required, some insurers do not distinguish between policy form. Give an example of a type of policy that will therefore have understated surplus required
|
Excess
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When deriving surplus required, some insurers rely only on true insurance risk. Give an example of a type of policy that will therefore have understated surplus required
|
Retro/Excess/LDD
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List 2 differences between fixed assets of a manufacturer and surplus of an insurer
|
1) A manufacturer can objectively measure the needed assets, whereas the needed surplus is an estimate based on expected future development
2) A manufacturer can divide the assets into product, but surplus cannot be divided into line. |
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How does "leverage" arise for an insurer?
|
Policyholders pay premiums before they receive a return from the insurer.
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List the parties interested in each of the ROR measures linked in Ferraris equation.
|
-ROE: Investors
-ROA: Society -ROS: Regulators |
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In the equation T/S = I/A + R/S (I/A + U/R), how can "U/R" be interpreted?
|
"Interest cost" incurred by the firm to use the reserves
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How can an insurer use Ferraris equation to decide whether to keep writing business?
|
In T/S = I/A + R/S (I/A + U/R), if the term in brackets is negative, the insurer should stop writing.
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What 3 types of ROR does Ferraris equation link
|
-ROE (T/S)
-ROA (I/A) -ROS (U/P) |
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2 equations by Ferrari to calculate Return on Equity
|
T/S = I/A (1+R/S) +U/P * P/S
T/S = I/A + R/S * (I/A + U/R) |
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|
Describe "Optimum Capital Structure"
|
Mix of Owners Equity and Liabilities that maximizes the value of the firm.
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What impact does writing more business have on the Capital Structure?
|
Increases liabilities relative to owners equity.
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Two factors which affect the value of the firm (and direction of impact)
|
1) Expected Earnings Stream (increase)
2. Rate at which this stream is discounted by the market (decrease) |
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Describe 2 ways writing more business changes firm value
|
1) increases earning stream, increasing value
2) increases volatility, increasing discount rate, reducing value. |
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Complication in relationship between increased writings and resulting discount rate
|
Increased writings usually results in increased diversification, which reduces volatility and therefore discount rate.
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According to Balcarek, 3 relationships ignored by Ferrari
|
1. Increase in P/S results in reduction to I/A
2. increase in U/P results in increase in P/S 3. increase in U/P results in increase in I/A |
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Briefly describe reinsurer actions under the Swap Technique
|
The reinsurer invests the funds to pay the losses in a risk free investment instead of the target investment.p
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Briefly describe reinsurers actions under the Put Option Technique
|
The reinsurer invests its funds in the target investment, and it also purchases an option that gives it the right to sell the target investment at a price, which would provide it with a return equal to the risk free rate of return.
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Advantage of reinsurers actions under Swap Technique
|
Reduction of Risk
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Disadvantage of reinsurers actions under Swap Technique
|
Loss of investment income
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2 advantages of reinsurer action under Put Option Technique
|
1) Increased investment return
2) Reduction in variance (compared to not purchasing option) |
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|
Disadvantage of reinsurers actions under Put Option Technique
|
Cost of Option
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Equation for A for Swap Technique, Constraint 1
|
A >= (s - mu)/ (1+y)
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|
List and briefly describe 2 constraint equations
|
1) Loss safety constraint: (1+rf)F>=s. The final value of the initial investment (F) at year end must be large enough to cover the losses at a specific safety level (s).
2. Investment Variance constraint: SD of IRR <= sigma*y, because the reinsurer does not want higher volatility from the contract compared to the target investment. |
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Equation for A for a Swap Technique, Constraint 2
|
A >= sigma_L / sigma_y
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Equation for R for Swap Technique, Constraint 1
|
R = (y-r_f) (s - mu_L)/(1+r_f)(1+y)
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Equation for A for Option Technique, Constraint 1
|
A >= 1/(1+y) * ((1+i)/(1+r_f) * s - mu_L)
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Equation for R for Swap Technique, Constraint 2
|
R = (y-r_f)/(1+r_f) * (sigma_L/sigma_y)
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Once the various As and Rs have been calculated, briefly describe the steps involved to calculate the Risk Load
|
1. For each financial technique, adopt the risk load from the more restrictive constraint (the constraint that produces the higher required assets)
2. Choose the preferred risk load from the suggested loads of the two techniques. |
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|
Equation for risk load in marginal surplus method
|
Risk Load = Multiplier * Marginal SD
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|
Which of the methods discussed by Mango are renewal additive
|
Shapely Value / Covariance Share
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|
Define "Renewal Additivity"
|
The sum of renewal risk loads of each risk is equal to the risk load for the aggregate portfolio.
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|
Explain why the Marginal Surplus method is not renewal additive
|
It is sub additive, and therefore understates the risk load in renewal.
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Explain why the Marginal Variance method is not renewal additive
|
It double counts the covariance, and therefore overstates the risk load in renewal.
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Explain how the Marginal Variance, Shapely Value, and Covariance Share methods allocate the mutual covariance upon renewal.
|
-Covariance: allocates the entire mutual covariance to each account.
-Shapely: allocates an equal amount of the covariance to each account -Covariance share: allocates a user specified portion of the covariance to each account. |
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|
2 ways to measure profit of an insurer
|
1) Profit
2) Rate of Return |
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|
Disadvantage of using profit to rate an insurer, compared to using Rate of Return
|
It is difficult to use "profit" to compare companies if we don't have other information
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|
3 examples of bases that can be used in the Rate of Return calculations
|
1) Equity
2) Assets 3) Sales |
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|
Describe "opportunity cost"
|
Since the policyholder pays premium before the losses are paid by the insurer, the policyholder is losing potential investment income.
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|
2 factors impacting opportunity cost
|
1) line of business
2) infrastructure investment |
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|
What discount rate should the opportunity cost be calculated at? Why?
|
The Risk Free Rate: the policyholder is not exposed to insurer's investment risk
|
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|
2 components of insurers investment earnings
|
1) investment income from policyholder funds
2) investment income from shareholder funds |
|
|
2 reasons that policyholders should only get credit for investment income from policyholder funds
|
1) shareholder funds do not belong to them
2) including shareholder funds will penalize high surplus insurers |
|
|
2 problems of using ROE to regulate an insurer
|
1) forces regulator to focus on ROE instead of rate equity
2) surplus needs to be allocated |
|
|
2 advantages of using ROS
|
1) understandable
2) does not require surplus allocation |
|
|
3 examples of changes to structure of industry if rates are inadequate
|
1) increasing size of residual market
2) Reducing degree of product diversity 3) reduced innovation |
|
|
Equation for adjusted underwriting profit provision under CY investment Income offset procedure
|
U = U_0 - i_AFIT * PHSF
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|
3 advantages of the CY Investment Offset Procedure
|
1) Data is easily obtained and verified
2) Since the figures are reported in filed documents, it is less likely that the insurer is making pessimistic projections in order to increase the profit provision 3) The calendar year investment portfolio yields are relatively stable |
|
|
Disadvantage of the CY investment Income Offset Procedure
|
Since CY results are retrospective, they may not be totally applicable to prospective ratemaking
|
|
|
2 Components of PHSF
|
1) PHSF on UEPR
2) PHSF on Loss Reserves |
|
|
2 advantages of the CY Investment Income Offset Procedure
|
1) Data easily obtained
2) Short and Straightforward calculation |
|
|
2 disadvantages of the CY investment Income offset procedure
|
1) Lack of economic theory supporting the calculation
2) Distorted if large change in volume or reserve adequacy |
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|
How does the "present value offset method" determine the profit provision
|
Calculates an investment offset to the traditional provision that is based on the difference of PVs of the line being priced, and a short tailed reference line
|
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|
3 advantages of Present value offset method
|
1) Accounts for investment income in a simple manner
2) not distorted by rapid growth/decline 3) No need to select target return or allocate surplus |
|
|
2 advantages of CY ROE Method
|
1) Figures are easy to verify
2) Produces an ROE similar to GAAP ROE used in other industries |
|
|
3 disadvantages of CY ROE Method
|
1) Distorted if large change in volume or reserve adequacy
2) Need to select target ROR 3) Need to select leverage ratio |
|
|
How does the "PVI/PVE Method" determine the Profit Provision
|
Selects to achieve the target Present Value Return (PVI / PVE)
|
|
|
In the PVI/PVE Method, to what point in time is income discounted?
|
End of first year
|
|
|
In the PVI/PVE method, to what point in time is Equity discounted?
|
Start of first year
|
|
|
How is Investment Income derived in the PVI/PVE Method
|
Investable Assets = Expense Res + Loss Res + UEPR + Surplus Prem Receivable
|
|
|
Advantages of PVI/PVE Method
|
Based on measure of ROR that is comparable to GAAP ROE
|
|
|
2 disadvantages of PVI/PVE method
|
1) Need to select discount rates
2) Need to select target ROR |
|
|
How does the "PV Cash Flow Return Model" determine the Profit Provision?
|
Produce a PV of total cash flow (discounted investment ROR) equal to the PV of changes in equity (discounted at target ROR)
|
|
|
In the "PV Cash Flow Return Model," to what point in time are the cash flows discounted?
|
Start of first year
|
|
|
In PV Cash flow return model, Cash Flow =
|
Underwriting Cash Flow + Investment Income - Tax
|
|
|
How is Investment Income derived in the cash flow return method
|
Based on surplus
|
|
|
Advantage of Cash flow return method
|
PV of Cash Flows is how most people think about underwriting profits
|
|
|
Disadvantages of Cash Flow Return Method
|
Not clear what type of profit is being measured, as cash flows do not have the same timing as GAAP income
|
|
|
How does the "Risk Adjusted DCF Model" determine the Profit Provision
|
Calculates a fair premium, and then derives a portion from that fair premium = Risk adjusted present value of underwriting cash flows + present value of taxes
|
|
|
In the "Risk Adjusted DCF Model," to what point in time are the Cash Flows discounted?
|
End of first year
|
|
|
How is Investment Income derived in the Risk Adjusted DCF Model?
|
Based on surplus
|
|
|
3 advantages of the Risk Adjusted DCF Model
|
1) Great intuitive appeal
2) Grounded in modern financial theory 3) Not necessary to determine a target ROR |
|
|
Disadvantage of the Risk Adjusted DCF Model
|
Hard to determine beta
|
|
|
How does the "IRR on Equity Model" determine the Profit Provision?
|
Selects a premium which achieves a target rate of return on the equity flows
|
|
|
Equity Flow =
|
Income - change in statutory surplus
|
|
|
How is Investment Income derived in the IRR on Equity Model?
|
Investable Assets = Expense Res + Loss Res + UEPR + Surplus - Prem Receivable
|
|
|
2 advantages of the IRR on Equity Model
|
1) The return to stockholders is similar to rate on a loan, so it is clear what is being measured
2) Reflects the accounting rules via their impact on the cash flows |
|
|
2 disadvantages of the IRR on equity model
|
1) Necessary to select a target return
2) Necessary to select a surplus requirement |
|
|
5 examples of Model Construction Questions
|
1) Should surplus be included in the model?
2) How should the surplus requirement be determined? 3) How should risk be incorporated into the model? 4) Is it better to use cash flows or income flows? 5) How to reflect income taxes? |
|
|
2 examples of parameter selection questions
|
1) What discount rate should be used?
2) What is the right target return? |
|
|
According to Robbin, 2 ways in which profit provisions can be regulated
|
1) Rate of return approach: rates should be regulated to ensure that companies are able to achieve an adequate return
2) Constrained free market theory: the premiums will move to an optimal level via market forces |
|
|
Definition of income, according to Roth
|
Annual increase in the net worth of the business from actual business operations
|
|
|
2 criteria of a "fair and reasonable return"
|
1) The return will be similar to that of other companies with similar risk
2) The return will be sufficient for the insurer to attract capital |
|
|
Differences of goals of stock and mutual insurer
|
-mutual insurers: provide availability of insurance
-stock insurers: profit maximization |
|
|
2 reasons that a higher portion of stock insurers have historically become insolvent than mutuals
|
1) stock companies are more focused on the commercial lines of business
2) Stock companies often have higher leverage |
|
|
Stock insurers need to increase surplus by an amount necessary to fund what 4 factors?
|
1) Expense & claims inflation
2) Increase in aggregate reserves 3) Increase in demand for insurance 4) dividends to stockholders |
|
|
Mutual insurers need to increase surplus by an amount necessary to fund what 3 factors?
|
1) Expense and claims inflation
2) Increase in aggregate reserves 3) Increase in demand for insurance |
|
|
Definition of "spot rate"
(BKM 15 & Hull 4) |
Interest taht applies from time 0 to time t.
|
|
|
Definition of "short rate"
(BKM 15 & Hull 4) |
Interest that applies during a future time interval.
|
|
|
Definition of "Treasury rate"
(BKM 15 & Hull 4) |
Rates earned on treasury bills and treasury bonds. This rate is essentially risk free.
|
|
|
Definition of LIBOR
(BKM 15 & Hull 4) |
London Interbank Offered Rate; the rate at which a bank will make a large wholesale deposit at another bank.
|
|
|
Definition of "Forward Rate"
(BKM 15 & Hull 4) |
Rate expected to apply during a future time period.
|
|
|
Terminal value of an amount "A" that is invested for "n" years at a rate of "R," compounded "m" times per annum
(BKM 15 & Hull 4) |
A*(1+R/m)^(n*m)
|
|
|
Terminal value of an amount "A" that is invested for "n" years at a rate "R" continuously compounded, is
(BKM 15 & Hull 4) |
A*exp(R*n)
|
|
|
Describe a forward rate agreement (FRA)
(BKM 15 & Hull 4) |
An over-the-counter agreement between two parties, to exchange a specified interest rate that applies to a specified pricipal during a specified future interval.
|
|
|
List 3 theories that can explain the shape of the yield curve
(BKM 15 & Hull 4) |
1. Expectations Hypothesis
2. Liquidity Preference 3. Segmentation Theory |
|
|
3 ways that stock prices are impaced by increasing interest/inflation
(Feldblum - Assets) |
1. Value of the firm: the firm assets increase in nominal value, causing stock prices to increase.
2. Supply and Demand: supply costs may increase, but demand may not. This will cause the firm value to fall. 3. Investment Strategy: Investors often shift their investments to long term bonds, which reduces the demand of stocks, and therefore stock prices fall. |
|
|
2 categories of appropriate investments to duration match inflation sensitive liabilities.
(Feldblum - Assets) |
1. shorter term securities
2. Inflation sensitive assets |
|
|
1 advantage of investing in stocks
(Feldblum - Assets) |
Higher yields
|
|
|
2 disadvantages of investing in stocks
(Feldblum - Assets) |
1) exposes investor to systematic stock market risks
2) higher transaction costs |
|
|
1 advantage of investing in real estate.
(Feldblum - Assets) |
Inflation Sensitive
|
|
|
3 disadvantages of investing in real estate
(Feldblum - Assets) |
1) investment usually limited by regulations
2) illiquid 3) requires investment expertise |
|
|
2 advantages of investing in short term bills/commercial paper
(Feldblum - Assets) |
1) short term duration, so appropriate for matching inflation sensitive liabilities
2) short duration, so not as sensitive to changing interest rates |
|
|
2 disadvantages of investing in short term bills/commercial paper
(Feldblum - Assets) |
1) lowest yields
2) higher transaction costs than long term bonds |
|
|
3 advantages of investing in long term bills
(Feldblum - Assets) |
1) higher yields
2) lowest transaction costs 3) held at amortized cost, so appears to be less volatile in financial statements |
|
|
2 disadvantages of investing in long term bills
(Feldblum - Assets) |
1) Lower yields than stocks
2) longer durations |
|
|
Why does Feldblum believe that duration matching is not as important as some of the other investment concerns for P&C insurers?
(Feldblum - Assets) |
P&C insurers are not subject to the risk of disintermediation. They can rely on cash flow from current premium and investment income to pay claims.
|
|
|
List 3 traditional investment concerns
(Feldblum - Assets) |
1) Maximizing expected returns
2) ensuring safety of principal 3) Balancing the risk of each class of securities |
|
|
2 components of the market value of a P&C company
Norris |
1. Portfolio Equity: currently booked assets - currently booked liabilities
2. Franchise equity: value of the net income from business not yet booked. |
|
|
3 methods to measure portfolio equity
Norris |
1. Statutory surplus: calculated using statutory accounting rules
2. Current value accounting: based on the market value of assets, and the undiscounted value of liabilities 3. Economic accounting: based on the market value of assets, and discounted liabilities. |
|
|
Equation for the MVS
Norris |
D_mvs = (D_mva*MV_a - D_mvl*MV_l)/MVS
|
|
|
Equation for DGs
Norris |
DGs = DG_mvs
|
|
|
2 ways to protect against interest rate fluctuations by managing DGs
Norris |
1) Select a certain gap depending on view of projected interest rates
2) target a MVS that is immune to rate changes (set the DGS to zero, or alternatively to the holding period) |
|
|
Equation for DGtrs
Norris |
DGtrs = DGs - H
|
|
|
Equation for DGel
Norris |
DGel = Dmvs - Dmva
|
|
|
3 strategies that an insurer can use to protect against the risk of unanticipated inflation
Norris |
1) Purchase securities with inflation dependant returns (eg stocks)
2) Purchase investments that roll over often 3) Maintain a contingency reserve |
|
|
Describe the term "franchise value."
(Panning) |
The economic value of the profits that will be earned in the future years from the future renewals of current policies.
|
|
|
2 components of the practical dilemma that is caused by franchise value
(Panning) |
1) The greater the franchise value of the firm, the more difficult it is to manage interest rate risk.
2) Reducing the duration of invested assets to offset the positive contribution of franchise value to the duration may puzzle regulators, as they only see the accounting numbers, and therefore do not account for the franchise value |
|
|
1 advantage of managing the duration via pricing policy
(Panning) |
Avoids rating agency and regulatory risk that are associated with managing the duration of the invested assets
|
|
|
1 disadvantage of managing the duration via pricing policy
(Panning) |
The desired combination of target return on surplus and target duration can be maintained only for small interest rate changes.
|
