Holding Period Return

The computation has three inputs: the value at the start of the period, the value at the end, and any cash distributed during the period. Add the ending value to the cash received, subtract the beginning value, and divide the result by the beginning value. Equivalently, sum the income yield and the capital-gain yield, each measured against the same starting base.

Two conventions matter. First, the denominator is always the amount actually committed at the start, not an average balance and not the ending value. Second, the measure is unitless and period-specific: it says nothing about how long the period lasted. A 5% return is 5% whether earned over a month or a decade, which is precisely why the raw figure must be labelled with its horizon before it can be compared with anything else.

Multiple consecutive returns combine geometrically. Convert each period return into a growth factor by adding one, multiply the factors across all periods, then subtract one to recover the cumulative return. This is the compounded, or time-weighted, result and it is the correct basis for measuring investment performance when there are no interim contributions or withdrawals.

To annualise, raise the cumulative growth factor to the power of one divided by the number of years and subtract one. For horizons shorter than a year, the exponent becomes the number of such periods in a year, so a quarterly return is compounded to the fourth power. Because compounding is multiplicative, annualising a short-horizon return upward tends to exaggerate it, and simply dividing a multi-year return by the number of years understates the true annual rate whenever returns are positive.

Total-return indices are constructed by chaining daily holding period returns that assume dividends are reinvested; price indices chain only the capital component. The same distinction separates a bond's coupon-inclusive return from its price move, and separates fund fact-sheet total return from a chart of net asset value alone.

The measure also underpins performance attribution and reporting standards. When cash flows in and out of a portfolio, the period is broken at each flow date and the resulting subperiod returns are chained, which removes the distorting effect of client contributions and isolates the manager's decisions. That chained figure is the time-weighted return. Its counterpart, the money-weighted return, is an internal rate of return and answers a different question: what the investor actually earned given the timing and size of their own cash flows.

Compute the return from a price pair and a dividend or coupon; decompose it into income and capital components; chain a sequence of returns and annualise the result; and reverse the process, deriving a periodic return from an annual figure using a fractional exponent rather than division.

Beyond arithmetic, be ready to choose the appropriate measure. If asked to evaluate a manager, use the chained, time-weighted figure. If asked what the investor earned, solve for the internal rate of return. Recognise that a nominal return becomes a real return by dividing the nominal growth factor by the inflation growth factor and subtracting one, not by subtracting inflation directly. Finally, treat leverage explicitly: with borrowed funds, the denominator is the investor's own equity, which magnifies both gains and losses.