CHAPTER 9 Martellini Lecture

# CHAPTER 9 Martellini Lecture - CHAPTER 9 MARTELLINI...

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CHAPTER 9 MARTELLINI PERFORMANCE MEASUREMENT ON FIXED INCOME PORTFOLIOS RETURN MEASURES To calculate the return on an investment that involves one time period, must use the following formula: r t, t + 1 = (V t + 1 ─ V t + D t, t + 1 ) / V t V t = value of portfolio at date t or start date or an arbitrary start date D t, t + 1 = cash flow distribution between t and t + 1 V t + 1 = value of portfolio at most current date or end date or an arbitrary end date Alternative formula: HPR = (EV ─ BV + D istr ) / BV ARTITHMETIC RATE OF RETURN Consists of taking a simple equally weighted average of return over different time periods. Problem with this approach: may lead to misleading interpretations as seen in Example 9.1 on page 293. GEOMETRIC RATE OF RETURN Using a geometric average to calculate the return on a bond portfolio in a multi-period setting gives an accurate picture of the return on a portfolio. Two types of geometric rate of return: Value weighted Time weighted geometric average 1

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Value weighted, or dollar weighted rate of return , is the same as finding the IRR on a series of cash flows. See page 294 for equation. CF t = net cash flows (cash inflows ─ cash outflows) from the bond portfolio for dates t = 1, . . . . , T V 0 = the initial market value of the portfolio V T = the terminal value of the portfolio Time weighted rate of return : A measure of the compounded rate of growth of a portfolio Normally used to compare the returns of investment managers because the method eliminates the distorting effects of new money inflows Here assume a single investment at the beginning of a period and measuring the growth or loss of market value to the end of the period Assumption: All cash distributions (interest) are reinvested in the portfolio Assumption: Exactly the same periods are used for comparisons This calculation reflects reinvestment from one period to the next To calculate a time weighted rate of return: 1. Compute the returns between withdrawals 2. Assume that inflows and outflows take place at the end of a given period (whether a week or a month) 3. Compound the returns (geometric average) 4. If the time horizon is less than a year, must also annualize the performance See Example 9.2 on pages 294-295. 2
Key ideas: The value weighted rate of return and the time weighted rate of return are equal if there are no withdrawals or contributions over the evaluation period and all investment is reinvested The dollar weighted rate of return is a better measure of performance when the investor or portfolio manager has control over the inflows and outflows of money When the manager has no control over inflows or outflows of money (such as a pension fund manager), the time weighted geometric average should be used RISK ADJUSTED PERFORMANCE EVALUATION ABSOLUTE RISK ADJUSTED PERFORMANCE EVALUATION Prof. Markowitz introduced volatility as a natural measure of risk. Here volatility (σ) is

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CHAPTER 9 Martellini Lecture - CHAPTER 9 MARTELLINI...

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