Rate of Return

A holding period return compares what an investor ends up with to what was put in. For a single period, it is the income received during the period, such as dividends or coupons, plus the change in the asset's price, all divided by the starting price: R = (P₁ − P₀ + D₁) / P₀, where P₀ is the purchase price, P₁ the ending price and D₁ the income received.

The result splits into two parts: an income component, D₁ / P₀, and a capital gain or loss, (P₁ − P₀) / P₀. A gain is realized when the position is sold and unrealized while it is still held, but both count in the period's return. Returns for periods shorter or longer than a year are usually annualized before they are compared, by compounding the periodic figure over the number of periods in a year.

The word return covers two different numbers. An expected return is a forecast made before the period starts, based on the current price and the cash flows the investor anticipates, and is written E(R). A realized, or actual, return is measured after the period ends, from the prices and income that actually occurred. Decisions are made with expected returns; performance is judged with realized ones.

The two rarely match, and the difference between them is the essence of risk. A portfolio expected to earn 8% may return 20% or lose 10% in a given year. When reading a question, check which one is meant: an expected or required return feeds a valuation, while a realized return describes what has already happened.

Three rate-like terms are easy to blur. An interest rate is agreed in advance between borrower and lender and is the price of money for the period; a fixed-rate deposit at 4% pays 4% whatever markets do, provided the bank pays. A yield is computed from an instrument's current market price, such as a bond's yield to maturity or a stock's dividend yield, and changes whenever the price changes. A return is the outcome of holding the asset over a period.

The distinction matters most for bonds. Yield to maturity is a promised figure: the realized return equals it only if the bond is held to maturity, every payment arrives in full and on time, and each coupon is reinvested at that same yield. When rates move, the realized return departs from the yield quoted at purchase.

A headline return is only the start. A gross return is measured before management fees and other costs; a net return is what the investor keeps after them. An after-tax return deducts taxes on income and realized gains. A real return removes inflation: (1 + R) / (1 + inf) − 1, which is close to, but not the same as, simply subtracting the inflation rate.

Leverage magnifies everything. Borrowing to buy more of an asset raises the return on the investor's own capital when the asset earns more than the cost of the borrowing, and deepens the loss when it earns less. Candidates should be able to compute each adjustment and recognize which version of return a question is quoting.