Portfolio Management Case Study

Asset liability management:
It is the management of assets and liabilities in such a way that the net earnings from interest is maximized and minimizing the overall risk associated with it. So it is a tool that helps bank to take business decisions in a known window with the view of the risk that the bank is associated with.
Portfolio management:
Portfolio is a combination of financial instruments like bonds, common stocks, banknotes, debentures and other instruments. The process of obtaining optimum returns with minimum risk from the combination of various portfolios is called portfolio management.
Immunization is a strategy that equalize the duration of assets and liabilities such that it minimizes the impact of interest rates
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Duration determines the sensitivity of prices to change in interest rates by representing the percentage change in value in response to changes in interest rates.
Portfolio managers who use an immunization strategy frequently takes into account Macaulay duration. The Macaulay Duration of a collection of cash flows is a weighted average of time periods, at which the cash flow occur, where the weights are the present values of cash flows with respect to the sum of the present value of all the cash flows i.e. the value of cash flow at time 0.
Macaulay’s Duration is represented by, D:

Where Current Bond price equals

Where t= respective time period C= Periodic coupon period y= Periodic yield n= total number of periods M= maturity value.
Or in words, Duration = Present value of a bond’s cash flows, weighted by length of time to receipt and divided by the bond’s current market value.
Let us take an example to understand
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As changing interest rates affect yield, fluctuation in interest rates will affect Duration. So Macaulay formula is modified to study the duration change for every percentage change in yield.
We know that Bond price and interest rates are inversely related so modified duration changes inversely with every 1% percentage change in yield. Hence this modified Duration is apt for investors to measure the volatility of a particular bond. Modified duration is represented as Where, YTM= yield to maturity n= number of coupon periods per year

From our previous example we get, Modified duration = 4.2177/ (1+0.08/2)

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