How Expected Rates of Return Affect the Prices of Stocks and Bonds
by
Charles Lamson
Stocks and bonds are two major, long-term financial instruments. Stocks represent ownership of part of the issuing firm, whereas bonds represent debt of the issuer, whether it is a firm, government entity, or other deficit spending unit (DSU). To streamline the analysis, we focus on how stock and bond prices are related, while recognizing that the analysis could easily be extended to other long-term financial instruments.
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Stocks
The size of a shareholder's ownership position depends on the number of stock shares owned. For example, if there are 1,000 shares outstanding, a stockholder who owns 100 shares, in effect, owns 10 percent of the firm. The value of each share---and therefore, the value of the stockholder's holdings in the corporation---depends on the prevailing price of the firm's stock. If, for example, the price is $50 per share, the total value of the stockholder's 100 shares is $5,000. The key question is what determines the price per share.
Outstanding shares of stocks are traded on organized exchanges such as the New York Stock Exchange or by networks of brokers and dealers around the country. Stock prices fluctuate daily, some going up, some going down as financial investors buy and sell shares of various corporations. In part, those fluctuations occur because a share of stock represents a claim on the earnings of a firm. Tangible evidence of this sharing of earnings comes in the form of dividends, which are a distribution of profits to stockholders. If earnings prospects are improving, the share price and dividend paid per share may also be rising. Financial investors will be attracted by the improved outlook (profitability) for the firm.
In general, as current and expected future earnings rise, stock prices also rise, and as current and prospective earnings decline, stock prices decline. A growing economy means that sales, production, and incomes are expanding, while a declining economy means the opposite. Since expected earnings also rise when the economy is expected to grow, and tend to fall when the economy is expected to contract, there is often a positive correlation between the growth of real national income and stock prices.
A portfolio usually consists of both stocks and bonds. How would you go about managing such a portfolio? More specifically, how would you decide whether to purchase stocks or bonds. We hope that you would compare the expected rates of return on the different types of financial assets, selecting those with the highest expected return consistent with the risk you are willing to take.
What is the expected return on stocks? Generally speaking, the expected return on a share of stock, say over a year, is the expected dividend plus the expected change in the price of the stock, all divided by the share price at the time of purchase. For example, if you pay $50 a share, the expected dividend is $1 per share, and you expect the price to rise $3 over the year, the expected return is 8 percent [($1 + $3)/$50 = .08 = 8 percent]. Now would be a good time to look at Exhibit 1, which examines this relationship.
1. The Expected Return to Owning Stock
As the body of The Financial System & the Economy by Burton & Lombra explains, the expected return on owning a share of stock over, say, one year is the expected dividend plus the expected capital gain or loss, divided by the share price at the time of purchase. Thus, whenever either factor changes, the expected return will change.
Assume that the stock originally costs $50 per share. The table above shows the rate of return for owning the stock, given various expected dividends and expected price changes (the capital gains or losses).
If actual dividends or actual capital gains and losses turn out to be different from those expected, the actual return will be different from the expected. Needless to say, all investors hope that actual dividends and capital gains turn out to be higher than expected rather than the reverse.
Bonds
With regard to bonds, the expected return is the current interest rate. Bonds represent long-term debt and pay a fixed annual coupon payment. The coupon payment is the product of the face value of the bond multiplied by the coupon rate. Bondholders are entitled to be paid the coupon payment before dividends are paid to stockholders. The coupon rate is the interest rate at the time the bond is originally issued and usually appears on the bond itself. The coupon rate is not the same thing as the current interest rate if interest rates have changed since the bond was issued.
For example, if the face value of a bond is $1,000 and the coupon rate is 6 percent, then the coupon payment is $60, since $60 divided by $1,000 is equal to 6 percent ($60/$1,000 = .06). This coupon does not change even if interest rates change after the bond has been issued. However, the bond's price will change whenever interest rates change or if the issuers ability to make the agreed upon interest or principal payments comes into question.
As portrayed in Exhibit 2, the expected return on bonds is the coupon rate plus the expected percentage in the bond's price over the course of the year.
2. The Expected Return on Bonds
Let us assume you purchase a $1,000 newly issued 30-year bond described above with a 6 percent coupon rate. You expect interest rates to fall to 4 percent during the next year. If interest rates fall to 4 percent the price of the bond would approach $1,500, since $60 divided by $1,500 is equal to 4 percent ($60/$1,500 = .04). In other words, prices of previously issued bonds adjust so that they pay the new prevailing interest rate. The expected return on the bond is equal to the coupon rate (6 percent), plus the expected percentage capital gain from the change in interest rates. In our example, the new interest rate is 4 percent and the expected percentage capital gain is [($1,500 - $1,000)/$1,000 = .5 = 50 percent]. Thus, the expected return to owning the bond over the year is the coupon rate (6 percent) plus the expected percentage capital gain (50 percent), or 56 percent.
To see how bond prices fit into the picture, assume that the current interest rate on bonds is 6 percent and that the expected return on stock is 8 percent, with the typical stock costing $50 and the expected dividend equal to $4. We also assume for simplicity that the expected capital gain is zero and that stocks and bonds have the same degree of liquidity. Assuming that stocks are riskier than bonds and that the portfolio managers must be compensated a percent for the additional risks of owning stocks, when bonds pay a 6 percent return and stocks pay an 8 percent return, the typical portfolio manager is indifferent between stocks and bonds. He or she will presumably hold some of each because the risk-adjusted returns are equalized. Equation (1) depicts this situation:
(1) Risk-adjusted return on stocks = Risk-adjusted return on bonds
Nominal return on stocks - compensation for higher risk of owning stocks = risk-adjusted return on bonds
(8 percent - 2 percent) = 6 percent
Now suppose that the Fed decides to pursue a more expansionary monetary policy. The initial result of this is a decline in the interest rate on bonds to 4 percent and a reduction in the risk-adjusted return on bonds from 6 percent to 4 percent. The fall in the interest rate will tend to raise stock prices through two channels.
First, the expected return on bonds is now below the risk-adjusted expected return on stocks. Given the substitutability of stocks for bonds in investors' portfolios and the expected return on stocks, the demand for stocks will rise, tending to raise stock prices. Within the confines of our simple example, we can even say how high stock prices will rise: stock prices will rise until the expected return on stocks is again 2 percent higher than the expected return on bonds (4 percent). This will occur when the price of our typical share of stock rises to $66.67 equals 6 percent ($4/$66.67 = .06).
Second, the fall in the interest rate will be expected to raise the demand for goods and services and increase the sales and earnings of firms. With earnings expected to rise, dividends will also be expected to rise. This reinforces the first effect. For example, if the dividend is expected to rise to $5 per share, then financial investors will be willing to bid up the price per share even further to $83.33 because $5 is divided by $83.33 is equal to 6 percent ($5/$83.33 = .06 = 6 percent). Again, after stock prices have adjusted to the change in interest rates, the risk-adjusted return on stocks will be equal to the risk-adjusted return on bonds.
Assuming you and other portfolio managers would like to have owned the stock before all this occurred, you can see now why actual and expected changes in the interest rate get so much attention in the stock market.
In the real world, there are many types of long-term financial instruments that offer varying degrees of risk and liquidity. Because of the substitutability of various financial instruments, prices of financial instruments will adjust so that returns to owning different instruments are equalized after adjustments have been made for differences in risk and liquidity. In other words, in financial markets risk - and liquidity-adjusted rates of return are equalized.
Prices of long-term financial instruments change as current and future expected earnings change. If interest rates fall, prices of previously issued bonds rise, and vice versa. If current and expected future earnings rise, ceteris paribus, stock prices also rise, and vice versa. In managing a portfolio, market participants compare expected rates of return and select those financial assets with the highest expected return and select those financial assets with the highest expected return, consistent with varying degrees of risk and liquidity. Stock and bond prices adjust until the portfolio manager is indifferent between stocks and bonds. If interest rates change, ceteris paribus, stock prices also change. When full adjustment has occurred, differences in returns on various financial instruments reflect differences in only risk and liquidity
*SOURCE: THE FINANCIAL SYSTEM & THE ECONOMY, 3RD ED., 2003, MAUREEN BURTON & RAY LOMBRA, PGS. 176-180*
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