Performance Evaluation and Active Portfolio Management
BM 410 Investments
Homework 25

Homework 25; Read Chapter 20

1. Consider the following data for a particular sample period: Portfolio P Market
Average return 35% 28%
Beta 1.2 1.0
Standard Deviation 42% 30%

Calculate the following performance measures for P and the market: Sharpe, Jensen (alpha), and Treynor. The T-bill rate during the period was 6%. By which measures did P outperform the market.

Sharpe = (rp – rf )/ sd
Portfolio (35-6)/42 = .69
Market (28-6)/30 = .73
Jensen = rp – [rf + ßp (rm – rf)]
Portfolio alpha = 35 – [6 + 1.2 (28-6) = 2.6%
Market alpha = 0
Treynor = (rp – rf )/ ßp
Portfolio (35-6)/1.2 = 24.2
Market (28-6)/1.0 = 22.0

The portfolio outperformed the market in terms of the Jensen’s alpha and the Treynor measure, but not the Sharpe ratio.

2. Consider the following information regarding the performance of a money manager during a recent month. The equity index is the S&P500, Bonds the Salomon Brothers Index, and cash is the Lehman Cash. Asset Class Actual Actual Benchmark Benchmark Return Weight Weight Return
Equity Fund 2.0% .70 .60 2.5%
Bond Fund 1.0% .20 .30 1.2%
Cash Fund 0.5% .10 .10 0.5%

a) What was the managers return in the month? What was the over/underperformance?
b) What was the contribution of security selection to relative performance?
c) What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contributions equals her total excess return relative to the bogey.

a) What was the managers return in the month? What was the over or underperformance? The managers return was (2.0%*.7) + (1.0%*.2) + (.5%*.1) or 1.65%. The index return was