Over multiple years To
annualize a holding period return means to find the equivalent
rate of return per year. Assuming income and capital gains and losses are reinvested, i.e. retained in the portfolio, then: :\text {Annualized rate of return} = \left( \frac {\text{end value}} {\text {initial value}} \right) ^ \frac {1}{t} - 1 ::=\left(\text {holding-period return} + 1 \right)^{\frac{1}{t}} - 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_{1}\right)\left(1+HPR_{2}\right)\left(1+HPR_{3}\right)\left(1+HPR_{4}\right)
Example with income not reinvested 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: ($98 – $100 + $1) / $100 = -1% Since the final stock price at the end of the year is $99, the annual holding period return is: ($99 ending price - $100 beginning price + $4 dividends) / $100 beginning price = 3% If the final stock price had been $95, the annual HPR would be: ($95 ending price - $100 beginning price + $4 dividends) / $100 beginning price = -1%. ==See also==