finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...

, holding period return (HPR) is the

return Return may refer to: In business, economics, and finance * Return on investment (ROI), the financial gain after an expense. * Rate of return, the financial term for the profit or loss derived from an investment * Tax return, a blank document or t ...

on an

asset In financial accountancy, financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value ...

portfolio Portfolio may refer to: Objects * Portfolio (briefcase), a type of briefcase Collections * Portfolio (finance), a collection of assets held by an institution or a private individual * Artist's portfolio, a sample of an artist's work or a ...

over the whole period during which it was held. It is one of the simplest and most important measures of investment performance. HPR is the change in value of an investment, asset or portfolio over a particular period. It is the entire gain or loss, which is the sum

income Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms. Income is difficult to define conceptually and the definition may be different across fields. For ...

and

capital gains Capital gain is an economic concept defined as the profit earned on the sale of an asset which has increased in value over the holding period. An asset may include tangible property, a car, a business, or intangible property such as shares. ...

, divided by the value at the beginning of the period. :HPR = (End Value - Initial Value) / Initial Value where the End Value includes income, such as dividends, earned on the investment: :

HPR_n \ = \ \frac

where

P_n

is the value at the start of the holding period and

Income + P_

is the total value at the end of the holding period.

Annualizing the holding period return

Over multiple years

To ''annualize'' a holding period return means to find the equivalent

rate of return In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment, such as interest payments, coupons, ca ...

per year. Assuming income and capital gains and losses are reinvested, i.e. retained in the portfolio, then: :

\text  = \left( \frac   \right) ^ \frac  - 1

=\left(\text  + 1 \right)^ - 1

''t'' being the length of the holding period, measured in years. For example, if you have held the item for half a year, ''t'' would equal 1/2, so 1/''t'' would equal 2. (However, investment performance professionals generally advise against quoting annualized return over a holding period of less than a year).

From quarterly holding period returns

To calculate an annual HPR from four quarterly HPRs, it is necessary to know whether income is reinvested within each quarter or not. If HPR1 through HPR4 are the holding period returns for four consecutive periods, assuming that income is reinvested, the annual HPR obeys the relation:

1+HPR=\left(1+HPR_\right)\left(1+HPR_\right)\left(1+HPR_\right)\left(1+HPR_\right)

To the right is an example of a stock investment of one share purchased at the beginning of the year for $100. Assume dividends are not reinvested. At the end of the first quarter the stock price is $98. The stock share bought for $100 can only be sold for $98, which is the value of the investment at the end of the first quarter. This is less than the purchase price, so the investment has suffered a capital loss. The first quarter holding period return is:

References

{{DEFAULTSORT:Holding Period Return Investment Mathematical finance