2. EAR, Cumulative Rates Return

Question 0

What is an effective annual rate? How is calculated?

Answer 0

Effective Annual Rate

1. this method is the correct way to annualize a rate of return.
2. Rear = (1 + HPR)^(t/#) - 1
   Where Rear = effective annual rate
   t = time period implied (i.e. months, quarters, days, etc.)
   # = time period referenced in scenario/problem

Question 1

What is an “APR?”

Answer 1

Annual Percentage Rate

1.A simple but misleading way to compute the annualized rate of return

2. APR = HPR * #
   where APR = annual percentage rate
   HPR = holding period return
   # = number of periods in a year

Question 2

What do you do if the holding period is defined in terms other than months?

Answer 2

If the holding period is defined in terms other than months, then the numerator and denominator must be changed.

1. If in quarters, the numerator will be 4.
2. If in days, the numerator will be 365.

Question 3

What are the three steps for converting monthly and quarterly rates to annual rates?

Answer 3

Converting Monthly and Quarterly Rates of Return to Annual Rates

The 3-step calculation (monthly):
1) Compute the 12 monthly return relatives
2) Compute the HPRR for these 12 return relatives
3) Subtract 1

Question 4

What is the modest common model for an expected return?

Answer 4

Expected Return – the most common model for expected return is to think of future returns as forming some sort of probability distribution and then to take the probability weighted average of this distribution.

Question 5

What are continuous probability distributions?

Answer 5

Continuous (think “nonstop”) Distribution
1.allows for the possibility of any potential rate of return.
2.More realistic than a discrete distribution in relation to an investment’s rate of return. For simplicity, discrete distributions are used in the text.

Question 6

What are discrete probability distributions?

Answer 6

Discrete (think “isolated”) Distribution

-each possible future rate of return can be identified and the associated probability can be stated.

Question 7

What is the formula for a Expected Return with a Discrete probability distribution?

Answer 7

On page 3 of ch 2 notes

Question 8

When is a “mean return” used as opposed to an “expected return”?

Answer 8

Note: The terms mean return and expected return, as well as their symbols, R and E(R), are sometimes used interchangeably, although they are different.

1.Mean Return used for ex post data
2.Expected Return used for ex ante data

Example: If we calculate that over the past 5 years, a stock has provided a mean return of 8.5 percent, we will likely say that the expected return for this security is also 8.5 percent.

Question 9

How is the rate of return on a portfolio measured?

Answer 9

The rate of return on a portfolio can be measured in the same way as the return on a single investment.

Question 10

Example of measuring rate of return for a portfolio:

You are reviewing the monthly statement of Joan Gitman. At the beginning of the month, her portfolio was worth $158,212. Joan received $1,524 in interest and dividends during the month (which were paid directly her). The ending value of the portfolio was $161,918. What was her PPR for the month?

Answer 10

PPR = (Period’s income + Period’s change in value) / Beginning-of-period value

Period income=1,524
Period’s change in value =161,918 - 158,212
Beginning-of-period value = 158,212

PPR = (1,524 + [161,918 – 158,212]) / 158,212 = .0331, or 3.31%