Calculating the value of $1 invested

[Pages:3]Calculating the value of $1 invested

A step-by-step approach to comparing investment performance to the market using time-linked returns

Prepared by Pamela Peterson Drake A common method of comparing investment performance is to determine the value of a fixed investment amount (e.g., $1 or $100), in a stock by compounding the successive returns. This type of analysis does not control for risk, but does provide data that can be used to determine returns in subperiods, as well as the entire period under study.

Step 1: Download return data for both the stock and the market

If you download the data from CRSP, you will have the month end date, the holding period return on the stock, and the return on the market for each selected month or date. Using monthly returns for IBM common stock and the CRSP value-weighted index,

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Step 2: Create time linked returns, beginning with the first month

The first month's value begins with $1, for both the stock and the market. Subsequent returns are linked through compounding.1

Step 3: Link monthly returns to compound values

Compound the returns by using the value in the cell above as the base and then multiplying this base by one plus the return on the current month. Repeat this for each cell to the end of your data.

1 If you want to use the value of $100 invested, change "1+b2" to "100*(1+b2)".

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Step 4: Compare the value of $1

The final value of $1 compounded through time provides a means of comparing two investments. For example, the value of $1 invested in IBM on January 1, 2004, produces a value of $1.53 at the end of 2009. In comparison, the value of $1 invested over the same time period in the market produces a value of $1.23 at the end of 2009.

We can also use this information to calculate the returns for any sub-period. For example, the value of $1 on January 1, 2004 is $1, but the value of this investment at the end of 2006 is $1.08. Therefore we have what we need to determine the average annual return over 2004, 2005 and 2006:

Present value = $1 Future value = $1.08 Number of years = 3 Solving for the rate, i, i = 2.599%.

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