Chapter 5: Risk, Return and the Historical Record

Question 1

What is the holding-period return (HPR) on a share of stock?

Answer 1

A rate of return over a given investment period.

Question 2

What is the formula for holding-period return (HPR)?

Answer 2

HPR =

(End price - Start price + Div.)/Start Price

Question 3

What are the different ways to measure investment returns over multiple periods?

Answer 3

There are 3:

1. Arithmetic Average
2. Geometric Average
3. Dollar-Weighted Return

Question 4

What is the formula for arithmetic average?

Answer 4

The sum of returns in each period divided by the number of periods.

Question 5

What is the formula for geometric average?

Answer 5

Solve for r(G)

r(G) = [(1+.10)x(1+.25)x(1-.20)x(1+.20]^(1/4) - 1 = 7.19%

Question 6

What is dollar-weighted return?

Answer 6

The internal rate of return on an investment.

Question 7

What is geometric average?

Answer 7

The single per-period return that gives the same cumulative performance as the sequence of actual returns. This is referred to as a ‘time-weighted average return’ b/c it ignores the year by year.

Question 8

What is the formula for dollar-weighted average return?

Answer 8

First, establish the net cash flow for each year:
Year 0: -1.0; Year 1: -.1; Year 2: -.5; Year 3: .8; Year 4: -.6+1.56=.96
The final year includes the sum of the final cash inflow plus the value of the p.f. at the end of the 4th year. The net cash flows are then used in the formula:

0 = -1.0 + [.1/(1+IRR)]+[-.5/(1+IRR)^2]+[.8/(1+IRR)^3]+[.96/(1+IRR)^4] = .0338 = 3.38%