Return calculations (tutorials #1 to #10)

In the first 10 tutorials, from #1 to #10, we dealt with basic return calculations. This post is a summary of what we have learned so far.

Tutorial #1: The net return NR_t over a single period t is calculated as:

NR_t = (P_t - P_t-1) / P_t-1

where P_t-1 and P_t are the prices at the start and at the end of the period respectively. The gross return GR_t is simply  equal to 1 plus the net return: 

GR_t  = 1 + R_t = P_t / P_t-1

Tutorial #2: If the asset pays dividends D_t during the period, we have to take that into account and calculate the total return, which consists of the dividend yield and the capital gains rate:

R_t = (D_t / P_t-1) + (P_t - P_t-1) / P_t-1

Tutorial #3: If the asset is a stock and if there was a stock split during the period, we have to take this into account as well when calculating the return.

Tutorial #4: Adjusted prices that take into account dividend payments and stock splits make return calculations easier. Yahoo! Finance provides adjusted price data free to internet users.

Tutorial #5: Investors usually distinguish between dollar returns and rate of returns. Given that the rate of return is equal to R_t, the dollar return is RDollar_t = R_t P_t-1.

Tutorial #6: Investors need to be wary of the inflation rate when calculating returns. Inflation rate I_t is defined as the rate of increase in the consumer price index CPI:

I_t = (CPI_t - CPI_t-1) / CPI_t-1

Tutorial #7: The nominal rate of return R_t does not take into account the effect of inflation whereas the real rate of return RR_t does. The real rate of return can be calculated as:

RR_t = [(1 + R_t ) / (1 + I_t )] - 1

Tutorial #8: If an investor buys an asset for $1 and sells it for $1.1 after 12 months, his holding period return HPR is 10% per year. This can also be obtained by compounding periodic returns:

HPR_T = Π (1 + R_t ) - 1   where   t ∈ [1, T]

Tutorial #9: When compounding periodic stock returns, it is normally assumed that dividend payments are reinvested in the stock.

Tutorial #10: Arithmetic average return tells an investor an asset's return in an average month during his holding period. Geometric average return tells him the average return he earned per period during his holding period.

Now that we are through with return calculations, in the following tutorials we will start looking at interest calculations.

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