These lectures cover how to compute dollar return on stocks, percentage return on stocks, risk premium, portfolio variance, normal distribution and market risk premium.
How to Calculate Percentage Return and Dollar Return | Corporate Finance
Risk Premium for Stocks | Corporate Finance
Variability of Stock Return and Standard Deviation | Corporate Finance
If you buy an asset of any sort, your gain (or loss) from that investment is called the return on your investment. This return will usually have two components. First, you may receive some cash directly while you own the investment. This is called the income component of your return. Second, the value of the asset you purchase will often change. In this case, you have a capital gain or capital loss on your investment.
It is usually more convenient to summarize information about returns in percentage terms, rather than dollar terms, because that way your return doesn’t depend on how much you actually invest.
The government borrows money by issuing bonds in different forms. The ones we will focus on are the Treasury bills. These have the shortest time to maturity of the different government bonds. Because the government can always raise taxes to pay its bills, the debt represented by T-bills is virtually free of any default risk over its short life. Thus, we will call the rate of return on such debt the risk-free return, and we will use it as a kind of benchmark.
The variance essentially measures the average squared difference between the actual returns and the average return. The bigger this number is, the more the actual returns tend to differ from the average return. Also, the larger the variance or standard deviation is, the more spread out the returns will be.
The way we will calculate the variance and standard deviation will depend on the specific situation. In this chapter, we are looking at historical returns; so the procedure we describe here is the correct one for calculating the historical variance and standard deviation. If we were examining projected future returns, then the procedure would be different.
For many different random events in nature, a particular frequency distribution, the normal distribution (or bell curve), is useful for describing the probability of ending up in a given range. For example, the idea behind “grading on a curve” comes from the fact that exam score distributions often resemble a bell curve.
This chapter has explored the subject of capital market history. Such history is useful because it tells us what to expect in the way of returns from risky assets. We summed up our study of market history with two key lessons:
Risky assets, on average, earn a risk premium. There is a reward for bearing risk.
The greater the potential reward from a risky investment, the greater is the risk.
These lessons have significant implications for the financial manager. We will consider these implications in the chapters ahead.
We also discussed the concept of market efficiency. In an efficient market, prices adjust quickly and correctly to new information. Consequently, asset prices in efficient markets are rarely too high or too low. How efficient capital markets (such as the NYSE) are is a matter of debate; but, at a minimum, they are probably much more efficient than most real asset markets.