Calculating Annual Returns and Compounding Holding Period Return

Summary

The document works through a three-year stock holding period with changing prices and annual dividends. It shows how to calculate each year’s total return by adding that year’s dividend to the ending share price, subtracting the starting price, and dividing by the starting price. The stated yearly returns are then linked through compounding to obtain the holding period return.

The example’s timeline makes clear that each annual return uses the price at the beginning of that year as its denominator. Multiplying one plus each period’s return and subtracting one captures reinvestment-style compounding across periods. The result depends on the given prices and dividends and assumes the annual returns are compounded; the document does not discuss taxes, transaction costs, or alternative dividend reinvestment assumptions.

Key ideas

• Each period’s total return includes the dividend paid during that period.
• Calculate annual return relative to the price at the start of the year.
• Link annual returns by multiplying their gross return factors.
• Subtract one from the compounded gross return to get the holding period return.
• The worked example does not account for taxes or trading costs.

Tags

# Holding Period Return


# Holding Period Return












Bought stock for $12.00$/share. Sold 3 years later at $20$/share. Paid $1$ dividend each year for 3 years. Stock's value at the end of the first year was $18$ and $15$ at the end of the second. Find the holding period of return.

In this example, the work provided is below:

r1= 58.33% r2=-11.11% r3=40%

so HPR=(1.5833*.8889*1.40)-1 = 97.04%

I understand how to find the HPR, but am unsure how r1, r2 and r3 were obtained. I understand this is probably a bit trivial but I am new to this stuff so any help would be great, thanks!

## Answer by Alex C (score 1, accepted)

https://quant.stackexchange.com/a/44764

Make a time line like this:

```
Time  T0      T1        T2         T3
Price 12      18        15         20
Div            1         1          1
```

Then calculate R1 = (19-12)/12 = 0.5888

R2= (16-18)/18 = -0.1111

R3 = (21-15)/15 = 0.4000

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.