# Investment Returns

An **investment return** on a financial instrument is the amount of money earned by the instrument over a given time period. A financial instrument, such as a stock or bond, may pay dividends or interest, and may appreciate or depreciate in price in the secondary market. Hence, the investment return equals income received minus its cost. Income received would include any **current income**, such as dividends or interest payments, plus any capital gain or loss if the instrument is sold in the secondary market or, in the case of debt securities, if any principal payment is greater or less than its initial cost. Hence:

Total Return = Current Income + Capital Gains - Capital Losses

However, the **rate of return** will depend on the total return divided by the amount invested.

Rate of Return = (Current Income + Capital Gains - Capital Losses) / Amount Invested

## Real Rate of Return and the Inflation Premium

**Inflation** is the general increase in prices of goods and services, and reduces the purchasing power of the dollar. **Deflation** is the opposite, but generally happens only for short periods of time — most of the time, inflation prevails.

If an investment only yielded the inflation rate, then there would be no increase in purchasing power for the investor. There would be little incentive to invest except for the **inflation premium**, which is the part of the return necessary to maintain purchasing power parity for the future. However, without a real return, money would mostly be spent rather than invested. Hence, investors demand a **real rate of return** that exceeds the inflation premium.

Real Rate of Return = Total Rate of Return – Inflation Rate

Thus, investment returns must be at least as great as the **expected inflation premium**, which is the amount of return necessary to cover the expected rate of inflation for the near future.

## Investment Risk and the Risk Premium

Different investments differ in their risk. Some securities, such as U.S. Treasuries are considered risk-free, at least of credit default, whereas with other investments, such as options, an investor will often lose all invested capital.

Generally, higher risk investments potentially yield a higher return. For instance, U.S. Treasuries yield the lowest returns because they are considered free of credit default risk, since they are backed by the full faith and credit of the United States government. Small company stocks, on the other hand, have historically yielded much greater returns, but many of them lose money.

People expect riskier investments to have higher **expected returns**. This expectation is reasonable because if investments that differed only in their risk yielded the same returns, people would only invest in the safer securities. Consider 2 bonds with different amounts of expected risks, but paying the same nominal yield of 6%: corporate bond A has a credit rating of AAA and corporate bond B has a credit rating of BBB. Both issuers offer their bonds for $1,000. Their credit ratings differ because a credit rating agency decided that the risk of default for Corporation B exceeds it is for Corporation A, which is why its bonds have a lower credit rating. But why would an investor buy Corporation B's bond over Corporation A's for the same price with the same nominal yield? The result would be that corporation A probably could sell all its bonds, whereas Corporation B would have to lower its price to sell its bonds. By lowering the price below $1,000, its bonds will have a true yield that is higher than its nominal yield, and the price differential between the 2 bonds, and therefore, the differential between their true yields must be great enough to compensate investors for the greater expected risk of Corporation B's bonds over that of Corporation A's. Hence, investors require a return that is commensurate with the risk of the investment.

The risk premium depends not only on the **issuer of the security**, but also on the **type of security**. Bonds issued by a corporation, for instance, are considered safer than its stock because the corporation has a legal obligation to pay interest and principal, and if the corporation goes bankrupt, then bondholders have a priority claim over the stockholders to the residual assets of the corporation. Therefore, stockholders bear greater risk of losing their investment, so they will only buy or hold the stock if they think that it will yield a return greater than its bonds.

Because U.S. Treasuries are considered free of default risk, the market rates of Treasuries are considered the **risk-free rate**. All other investments pay a higher rate to compensate investors for the greater risk of default, or loss of capital. So investors demand a **required return** that is equal to the risk-free rate plus the amount necessary to compensate investors for the increased risk — the **risk premium**.

Required Return = Risk-Free Rate + Risk Premium

Since the risk-free rate is the sum of the real rate of return plus the expected inflation premium, the required return can be expressed thus:

Required Return = Real Rate of Return + Expected Inflation Premium + Risk Premium

## Holding Period Return

The **holding period** is the time interval that an investment is held. The **holding period return** is the investment return during the holding period. The **realized return** is the income received over the holding period, whereas a **paper return** is the potential return that would be earned if the investment were liquidated now.

The calculation for holding period returns is generally used for investments held for less than 1 year, and for which the time value of money is insignificant and the reinvestment of current income is not considered, which simplifies calculations.

Holding Period Return = (Current Income + Capital Gain or Loss) / Amount Invested

If a financial instrument pays current income, then the maximum return can only be earned if the current income is reinvested at the highest rate. The **reinvestment rate** is the rate that can be earned from income received from an investment that is reinvested; otherwise, the current income is not compounded. A **compounded rate of return** is earned when all current income is reinvested, yielding a higher return for the holding period. For instance, a 10-year corporate bond paying 6% would pay $30 in interest twice a year for 10 years, with the final payment including the principal of $1,000. At the end of 10 years, the bondholder would have received a total of $1,600 — a total of $600 in interest plus the $1,000 principal. However, an investment of $1,000 in a savings account paying 6% compounded semiannually would yield $1,806.11 at the end of 10 years, which is slightly more than an 8% bond would pay over the same period. Of course, this comparison disregards the opportunity cost incurred by reinvesting the money, which is not being able to spend it for 10 years.