Risk & Return

(Part 2)

Lecture 06

EFFECTIVE ANNUAL RETURN:

The return on an investment expressed on a per-year, or “annualized,” basis.

Till now we have discussed only returns of the overall investment. E.g. if the total percentage return on an investment is 35% and the investment was done for 6 months. Than it means that, this 35% return belong to the full life of investment i.e. 6 months.

Holding period: is the length of the time for which the investment was done.

For example: Suppose you bought 200 shares of Shah Companies, Inc. at a price of $48 per share. In three months, you sell your stock for $51. You didn’t receive any dividends. What is your return for the three months? What is your annualized return?

Solution:

First Calculating Percentage Return: With a zero dividend, you know that the percentage return can

be calculated as:

Percentage Return = 0.0625 * 100

Percentage Return = 6.25%

  This 6.25 percent is your return for the three-month holding

period.

Now Finding Effective Annual Return:

Formula for EAR is,

Where m is the number of holding periods in a year.

 

In our example, the holding period percentage return is 6.25 percent, or .0625. The holding period is three months, so there are four (12 months/3 months) periods in a year. We calculate the annualized return, or EAR, as follows:

AVERAGE RETURN:

Whenever we are having returns for more than one year, than at this particular time in order to make investment decision, it will be vice to calculate the average of the different returns you have in historical data.

The change in the annual return figure actually leads us to do so.

We have many measures of central tendency; we will discuss only two of them.

1. Arithmetic Return: The formula for arithmetic return is,

Year Returns

1 10%

2 12%

3 15%

4 (6%)

5 8%

6 4%

2. Geometric Average Return:

The formula for calculating geometric average return is,

Numerical:

Years Returns

1 10%

2 12%

3 3%

4 (9%)

Putting the values is in the above formula,

_ 1

Geometric Average Return = [1.10 + 1.12+ 1.03 – 1.09] ^ ¼ -1

Geometric Average Return = 3.66%

Now let us calculate the Arithmetic average return of the same data, in order to see is there any difference,

Arithmetic Average Return = 10% + 12%+ 3% - 9%/4

Arithmetic Average Return = 4%

BLUME’S FORMULA: Sometime our concerns are to forecast the future. There is a lot of confusion among analysts and financial planners.

i.e. Which one method is to be used for good estimations? The good news is that there is a simple way of combining the two

averages, which is called Blume’s formula. Presented by Marshal Blume’s. Journal of the American Statistical

Association, September 1974.

Where, T = Number of years for which you wish to find average possible return.

N = Number of years for which historical return data is taken.

R (T) = The forecasted average return for T period

Numerical based on Blume’s Formula:

Suppose that from 25 years of annual returns data, we calculated an arithmetic average return of 12% and a geometric average return of 9%. Now from these averages we wish to calculate average return forecasts for 1 year, 5 years and 10 years.

First Calculating for 1 year:

Secondly calculating for 5 years:

Thirdly calculating for 10 years: Class work. Do it now

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