4. Evaluating Portfolio Performance

Question 1

Explain why there can be substantial differences between the time-weighted and dollar-weighted rates of return.

Answer 1

The dollar-weighted rate of return will give heavier weight to the performance of the portfolio when the portfolio is larger in dollar value and less weight to the performance when it is smaller in dollar value. The greater the variation in the dollar value of the portfolio over time, the greater the chance for disparity between the two rates of return.

Question 2

If there are no interim cash flows, what is the relationship between the two rates of return?

Answer 2

If there are no interim cash flows, the two ways to measure the rate of return will be identical.

Question 3

A portfolio has a value of $235,000 at the start of the month, and an ending value of $260,000.

a. What is the rate of return for the period if $20,000 had been added to the portfolio on the first day of the month?
b. What is the rate of return for the period if, instead of the $20,000 being added at the start of the month, it is added to the portfolio on the last day of the month?

Answer 3

a. PPR = ($260,000 –$235,000 - $20,000)/$255,000 = .0196 or 1.96%
b. PPR = ($260,000 – $235,000 – $20,000)/$235,000 = .0213 or 2.13%

Question 4

In reviewing your client’s pension plan performance, you note the following
quarterly rates of return: 10 percent, –15 percent, 8 percent, and 5 percent.

What is the effective annual rate of return for the pension plan?

Answer 4

(1.1 x .85 x 1.08 x 1.05) – 1 = 1.0603 – 1 = .0603 or 6.03%

Question 5

Describe the Dow Jones Industrial Average and indicate its weaknesses as a major market index.

Answer 5

The DJIA is the sum of the prices of 30 stocks, divided by a number that has been
adjusted over the years to reflect stock splits and dividends paid in shares of stock. Its
weaknesses as a major market index include that the sample size of 30 is small, the stocks are not selected to represent the overall economy, it is price-weighted, which
means the highest-price stock has the most impact, and it does not incorporate dividends.

Question 6

How does the Russell 3000 Index relate to the Russell 2000 and Russell 1000 indices?

Answer 6

The Russell 1000 is composed of the 1000 largest stocks in the Russell 3000, and the Russell 2000 is composed of the remaining 2000.

Question 7

What is unique about the Value Line Index compared to all of the other indices?

Answer 7

It is the only index to provide equal weighting to all securities.

Question 8

What is the most comprehensive index of international securities?

Answer 8

MSCI EAFE

Question 9

Which company provides a large number of bond market indices?

Answer 9

Barclays Capital

Question 10

Describe the five reasons that actual portfolios tend to under perform or at least perform differently than market indices.

Answer 10

The five reasons are:

1. Indices pay no transaction fees or advisory fees.
2. Indices do not have to pay capital gains taxes over time.
3. Most indices have high levels of diversification, which individual portfolios cannot achieve.
4. Indices do not hold cash or bonds in their portfolios, and many people do.
5. Most portfolios have betas different than those of the indices.

Question 11

As the chair of the investment committee for your college, you are reviewing the performance of your three portfolio managers. The values of α and σε for the three managers are 1.8 percent and 2.2 percent for the first. 1.4 percent and 1.7 percent for the second, and 2.1 percent and 2.4 percent for the third.

Based on the information ratio, which one provided the best performance?

Answer 11

The information ratio is the ratio of alpha divided by the standard deviation of eta. So for the three managers, the ratios are:

First manager: 1.8/2.2 = .818
Second manager: 1.4/1.7 = .824
Third manager: 2.1/2.4 = .875

So in this case, the third manager performed best with the highest information ratio.