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 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 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 is greater than 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 the amount of risk involved. Some securities, such as U.S. Treasuries are considered to be risk-free, at least of credit default, whereas with other investments, such as options, an investor can 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 to be free of credit default, 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.
Hence, people select investments based on their expected returns, which are based on their expected risk for that investment. This must be so, because if different investments with differing amounts of 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 is greater than 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 of 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 to be safer than its stock because the corporation has a legal obligation to pay interest and principal, and if the corporation goes bankrupt, then the bondholders claim to the residual assets of the corporation are greater than the stockholders. Therefore, the stockholders have a greater risk of losing their investment, so they will only buy or hold the stock if they think that it will appreciate and yield a return greater than its bonds.
Because U.S. Treasuries are considered to be free of default risk, the market rates of Treasuries are considered to be 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 and 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 (HPR)
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 was 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
Internal Rate of Return (IRR)
The internal rate of return is the discount rate of the future cash flows of a financial instrument that would equal its present value. If the IRR, often called the hurdle rate in corporate finance, is greater than the required return, then the investment is a satisfactory investment, which is an investment whose present value of future payments is at least as great as its initial cost and the discount rate is at least equal to the required return.
For instance, if a corporate bond pays a nominal rate of 6% on a par value of $1,000, and an investor requires at least a 6% return, then if the bond cost $1,000 or less, then it would be a satisfactory investment, but if it cost more, then it would not, because the sum of the present value of its futures payments would still only equal $1,000 at 6%, so the discount rate would have to be less than 6% to yield its initial higher cost.
If the 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.
If current income is not reinvested, then it 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, if a 10-year corporate bond pays 8%, then it will pay $40 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 $1,800—a total of $800 in interest plus the $1,000 principal. However, if the investor had, instead, invested $1,000 in a savings account that paid only 6% compounded semiannually, he would have $1,806.11 at the end of 10 years. Of course, this comparison disregards the opportunity cost incurred by reinvesting the money, and not being able to spend it for 10 years.