Dollar vs rate of return (tutorial #5)

Investors usually distinguish between dollar versus rate of returns. The rate of return is a percentage figure, whereas the dollar return is, well, a dollar figure! Remember the Google example four posts ago. You had bought Google shares for $582.93 and sold them for $599.39, realizing a return of 2.82%. 2.82% is your rate of return. Your dollar return is 2.82% times your initial investment: 2.82% ($582.93) = $16.44. The general formula for calculating the dollar return is:

RDollar_t = R_t P_t-1

Remember that the total return is:

R_t = ( D_t + P_t - P_t-1 ) / P_t-1

Then plugging R_t into the first equation yields:

RDollar_t = D_t + P_t - P_t-1

This formula says that the dollar return is simply the price difference P_t - P_t-1 plus any dividends D_t received during the holding period. In our example D_t = 0, so the dollar return is P_t - P_t-1 = $599.39 - $582.93 = $16.46. This is not equal to $16.44, the figure we obtained above. Why is that? Relax, just a rounding error!

Rate of returns and dollar returns are both useful measures of investment performance, but a rate of return is particularly useful when comparing investments with different scales. Let us explain what we mean with an example. Imagine that you are chatting about the performance of your investments with a friend of yours, who is quite rich. Your friend is bragging that he has just sold a piece of art for $82,000. He had bought that piece for $80,000 a month ago. In other words, he has realized a dollar return of $82,000 - $80,000 = $2,000. But, how about his rate of return? It is ($82,000-$80,000) / $80,000 = 2.5%, which is actually inferior to what you realized from your investment in Google: 2.82%. So, you could tell your friend to stop bragging, because if you had $80,000 to invest in Google, your dollar return would be: 2.82% ($80,000) = $2,256, $256 more than your friend's dollar return.

Next tutorial: Inflation rate
Previous tutorial: Raw vs adjusted prices

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