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84 Cards in this Set
- Front
- Back
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Different debt instruments have very different... |
cash flows with very different timing |
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All else being equal, debt instruments are evaluated against one another based on the.. |
amount of each cash flow and the timing of each cash flow |
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This evaluation, where the analysis of the amount and timing of a debt instrument's cash flows lead to its yield to maturity or interest rate is called... |
present value analysis. |
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A dollar today... |
is worth more than a dollar tomorrow |
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The concept of present value is based on the commonsense notion that... |
a dollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today. |
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The notion of present value is true because you could... |
invest the dollar in a savings account that earns interest and have more than a dollar in one year. |
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The term present value can be extended to mean the... |
PV of a single cash flow or the sum of a sequence or group of cash flows. |
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There are four basic types of credit instruments which incorporate present value concepts: |
1. Simple Loan 2. Fixed Payment Loan 3. Coupon Bond 4. Discount Bond |
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Another name for a fixed payment loan |
Level Payment Loan |
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the amount of funds the lender provides to the borrower |
loan principal |
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the date the loan must be repaid |
maturity date |
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from initiation to maturity date |
Loan Term |
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the cash amount that the borrower must pay the lender for the use of the loan principal |
interest payment |
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Interest payment is how much you have to.. |
pay as compensation for the money |
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the interest payment divided by the loan principal |
simple interest rate |
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the percentage of principal that must be paid as interest to the lender |
simple interest rate |
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Convention is to... |
express on an annual basis |
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PV of future 1$ = |
n/(1+i)^n |
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For a simple loan... |
it's not simple interest, it's still compound interest |
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interest rate than equates today's value with present value of all future payments |
yield to maturity |
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require payment of one amount which equals the loan principal plus the interest |
simple loan |
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loans where the loan principal and interest are repaid in several payments, often monthly, in equal dollar amounts over the loan term |
Fixed-payment loans |
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Two examples of fixed payment loans |
mortgage car note |
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Installment loans, such as auto loans and home mortgages are frequently of the... |
fixed payment type |
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Coupon bonds... |
pay only interest and at the end, repays principal |
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fixed coupon payments at $c forever |
consol |
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P (consol)= |
C/i |
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P(coupon bond) = |
C/(1+i) + C/(1+i)^2...etc. |
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i (discount bond) = |
F-P/P |
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Most bonds are on a... |
semi-annual basis |
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YTm changes because... |
the prevailing market rate changes |
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To make up for the lost interest rate, you have to... |
cut the price |
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Three interesting facts about field to maturity and price |
When bond is at par, yield = coupon rate. Price and yield are negatively related Yield greater than coupon rate when bond price is below par value |
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If the interest rate i increases (YTM increases), the PV of any given cash flow is... |
lower, hence, the price of the bond must be lower |
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ic (current yield) = |
C/P |
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Current yield is just an... |
approximation for YTM |
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Two properties of Current Yield |
1. If a bond's price is near par and has a long maturity, then Current Yield is a good approximation. 2. A change in the current yield always signals change in same direction as yield to maturity. |
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What is the main use for Yield on a Discount Basis |
Main use is T-Bills |
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i(discount basis) = |
(F*P)/F * 360/(Number of days to maturity) |
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Two characteristics of Yield on a Discount Basis |
1. Understate yield to maturity; longer the maturity, greater is understatement 2. Change in discount yield always signals change in same direction as yield to maturity |
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Nominal rates have been... |
negative in the past |
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In November 1998, rates on Japanese 6 month government bonds were... |
negative. Investors were willing to pay more than they would receive in the future |
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What is the best explanation for negative rates? |
investors found the convenience of the bills worth something--more convenient than cash--but that can only go so far. |
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What is the real interest rate? |
Interest rate that is adjusted for expected changes in the price level |
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What is an approximation of the real interest rate |
ir = i - pi(e) |
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pi(e) is... |
expected inflation |
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Real interest rate more accurately reflects... |
the true cost of borrowing |
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When the real rate is low, there are greater... |
incentives to borrow and less to lend |
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Real interest rate tells us... |
how much more stuff we can buy |
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what is the exact version for real interest rate |
ir = (1+i)/(1+pi(e)) - 1 |
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What is the ex ante real interest rate? |
adjusted for expected level of inflation |
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What is the ex post real interest rate? |
What actually happened |
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What is the yield to maturity? |
the yield you get if you hold the item until it matures |
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Return = |
yield + Capital gains
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Return = |
C+FP - P/P |
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ic = |
C/Pt |
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G = |
FP- Pt/Pt |
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g = |
capital gains |
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ic = |
current yield |
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Return = |
income + (end price - beginning price)/Beg. price |
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Income |
coupon payment or dividend |
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When yield goes up... |
price goes down |
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Only bond whose return = yield is one... |
with maturity = holding period |
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For bonds with maturity > holding period... |
if i goes up P goes down implying capital loss |
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Longer is maturity, greater is... |
price change associated with interest rate change |
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Longer is maturity, more return.. |
changes with change in interest rate. |
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Bond with high initial interest rate can still have negative return... |
if i increases |
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Prices and returns more volatile for long term bonds because... |
they have higher interest rate risk |
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No interest rate risk for any bond whose... |
maturity equals holding period. |
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What happens with reinvestment risk? |
occurs if investor holds a series of short bonds over long holding period |
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Two points from Reinvestment risk |
i at which reinvest uncertain Gain from i increasing, lose when i decreases |
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What happens with reinvestment? |
you're not going to be able to get the same amount you were getting |
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Two points about duration |
1. All else equal, when the maturity of a bond lengthens, the duration rises as well. 2. All else equal, when interest rates rise, the duration of a coupon bond falls |
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When interest rates rise, you.. |
discount at a higher rate and the PV becomes relatively small |
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Relative to the lump sum payment at the end... |
the coupon payments are worth more |
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The higher the coupon rate on the bond.. |
the shorter the duration of the bond |
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Duration is additive: |
the duration of a portfolio of securities is the weighted average of the durations of the individual securities, with the weights equaling the proportion of the portfolio invested in each security |
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What a handy approximation for a change in the value of the secures vs. the change in interest |
%change in Price ~ -Dur * change in i/1 + i |
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The greater the duration of the security... |
the greater the percentage change in the market value of the security for a given change in interest rates |
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The greater the duration of a security, the greater its... |
interest rate risk |
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Long maturity bonds are more... |
volatile |
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What is the matrix for duration? |
Time|Cash flows|Present Value|Time weight|Time weight/price |
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Time weight = |
Time * Present value |
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Duration = |
Time weight/price |
