INVESTMENT MANAGEMENT PROCESS Setting investment objectives Establishing investment policy Selecting a portfolio strategy Selecting assets Managing and evaluating performance

1. Setting investment objectives For institutions such as banks and thrifts – dictated by nature of liabilities For Pension Funds – to generate sufficient cash flows to meet pension obligations For Life Insurance Companies – the basic objective is to satisfy obligations stipulated in policies and generate profits For Mutual Funds – Objectives are set forth in the prospectus – No specific liabilities

2. Establishing investment policy Asset allocation decision: cash equivalents, equities, fixed- income securities, real estate, and foreign securities Considerations – Client and regulatory constraints – Tax and financial reporting implications

3. Selecting a portfolio strategy – Passive rests on the belief that bond markets are semi-strong efficient current bond prices viewed as accurately reflecting all publicly available information Involves minimal expectational output e.g. Indexing – Active rests on the belief that the market is not so efficient some investors have the opportunity to earn above-average returns Involves forecasts of future interest rates, future interest rate volatility, or future yield spreads.

3. Selecting a portfolio strategy (contd.) – Enhanced Indexing/ Indexing Plus A primarily indexed portfolio but employ low-risk strategies to enhance the indexed portfolio’s returns – Structured Portfolio Strategies Used to fund liabilities. To achieve the performance of a predetermined benchmark – To satisfy single liability (Immunization) – To satisfy multiple future liabilities (Immunization, Cash flow matching, horizon matching) – Contingent Immunization Manager follows active strategy to point where trigger point is reached Switch made to passive strategy to meet minimum acceptable return

4. Selecting assets For e.g. In Active strategy – identifying mispriced assets Based on bond characteristics like coupon, maturity, credit quality, options embedded. Attempts to create an efficient portfolio

5. Managing and evaluating performance Involves measuring the performance and evaluating the performance to some benchmark e.g. Merrill Lynch Domestic Market Index.

Five Bond Pricing Theorems For a typical bond making periodic coupon payments and a terminal principal payment – THEOREM 1 If a bond’s market price increases then its yield must decrease conversely if a bond’s market price decreases then its yield must increase

Five Bond Pricing Theorems For a typical bond making periodic coupon payments and a terminal principal payment – THEOREM 2 If a bond’s yield doesn’t change over its life, then the size of the discount or premium will decrease as its life shortens

Five Bond Pricing Theorems For a typical bond making periodic coupon payments and a terminal principal payment – THEOREM 3 If a bond’s yield does not change over its life then the size of its discount or premium will decrease at an increasing rate as its life shortens

Five Bond Pricing Theorems For a typical bond making periodic coupon payments and a terminal principal payment – THEOREM 4 A decrease in a bond’s yield will raise the bond’s price by an amount that is greater in size than the corresponding fall in the bond’s price that would occur if there were an equal-sized increase in the bond’s yield the price-yield relationship is convex

Five Bond Pricing Theorems For a typical bond making periodic coupon payments and a terminal principal payment – THEOREM 5 the percentage change in a bond’s price owing to a change in its yield will be smaller if the coupon rate is higher

Duration Since price volatility of a bond varies inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective A composite measure considering both coupon and maturity would be beneficial

Duration (contd.) Developed by Frederick R. Macaulay, 1938 Where: t = time period in which the coupon or principal payment occurs C t = interest or principal payment that occurs in period t i = yield to maturity on the bond

Problem on Macaulay’s Duration Undiscounted Cash Flow TimePV FactorPresent ValuePV*T /1.1010*1/ /1.10^210*1/1.10^ /1.10^310*1/1.10^ /1.10^410*1/1.10^ /1.10^5110*1/1.10^

Problem (contd.) Macaulay’s Duration

Characteristics of Duration Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim payments – A zero-coupon bond’s duration equals its maturity An inverse relation between duration and coupon A positive relation between term to maturity and duration, but duration increases at a decreasing rate with maturity An inverse relation between YTM and duration

Duration in Years for Bonds Yielding 6% with Different Terms Term to maturity

Modified Macaulay’s Duration An adjusted measure of duration can be used to approximate the price volatility of a bond Where: m = number of payments a year YTM = nominal YTM

Problem on Modified Macaulay’s Duration

Duration and Price Volatility Bond price movements will vary proportionally with modified duration for small changes in yields An estimate of the percentage change in bond prices equals the change in yield time modified duration Where:  P = change in price for the bond P = beginning price for the bond D mod = the modified duration of the bond  i = yield change in basis points divided by 100

Duration and Price Volatility Where:  P = change in price for the bond P = beginning price for the bond D mod = the modified duration of the bond  i = yield change in basis points divided by 100

Duration and Price Volatility Longest duration security gives maximum price variation Duration is a price-risk indicator

Convexity Modified duration approximates price change for small changes in yield Accuracy of approximation gets worse as size of yield change increases – WHY? – Modified duration assumes price-yield relationship of bond is linear when in actuality it is convex. – Result – MD overestimates price declines and underestimates price increases – So convexity adjustment should be made to estimate of % price change using MD

CONVEXITY The relationship between convexity and duration YTM P 0

Convexity (contd.) Convexity of bonds also affects rate at which prices change when yields change Not symmetrical change – As yields increase, the rate at which prices fall becomes slower – As yields decrease, the rate at which prices increase is faster – Result – convexity is an attractive feature of a bond in some cases

Convexity (contd.) The measure of the curvature of the price- yield relationship Second derivative of the price function with respect to yield Tells us how much the price-yield curve deviates from the linear approximation we get using MD

REFERENCES Bond Markets, Analysis, and Strategies – Frank J. Fabozzi L. Fisher and R. L. Weil, "Coping with the Risk of Interest Rate Fluctuations: Returns to Bondholders from Naïve and Optimal Strategies," Journal of Business 44, no. 4 (October 1971): 418. Copyright 1971, University of Chicago Press.