Lecture 1 Notes part1 - Required knowledge PDF

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Net Present Value When we compute the value of a cost or benefit in terms of cash today, we refer to it as the present value (PV). Similarly, we define the net present value (NPV) of a project or investment as the difference between the present value of its benefits and the present value of its costs: Net Present Value: NPV= PV(Benefits) - PV(Costs) If we use positive cash flows to represent benefits and negative cash flows to represent costs, and calculate the present value of multiple cash flows as the sum of present values for individual cash flows, we can also wrile this definition as: PV(All project cash flows) That is, the NPV is the total of the present values of all project cash flows. The NPV Decision Rule Because NPV is expressed in terms of cash today, it simplifies decision making. As long as we have correctly captured all of the costs and benefits of the project, decisions with a positive NPV will increase the wealth of the firm and its investors. We capture this logic in the NPV Decision Rule: When making an investment decision, take the alternative with the highest NPV Choosing this alternative is equivalent to receiving its NPV in cash today. Accepting or Rejecting a Project. A common financial decision is whether to accept or reject a project. Because rejecting the project generally has NPV = 0 (there are no new costs or benefits from not doing the project), the NPV decision rule implies that we should Accept those projects with positive NPV because accepting them is equivalent to receiving their NPV in cash today, and Reject those projects with negative NPV; accepting them would reduce the wealth of investors, whereas not doing them has no cost (NPV = 0). If the NPV is exactly zero, you will neither gain nor lose by accepting the project rather than rejecting it. It is not a bad project because it does not reduce firm value, but it does not increase value either. Regardless of our preferences for cash today versus cash in the future, we should always maximize NPV first. We can then borrow or lend to shift cash flows through time and find our most preferred pattern of cash flows. Investor Risk Appetite and Risk Premium The notion that investors prefer to have a safe income rather than a risky one of the same average amount is called risk aversion. It is an aspect of an investor's preferences, and different investors may have different degrees of risk aversion. The risk premium of a security represents the additional return that investors expect to earn to compensate them for the security's risk. Because investors are risk averse, the price of a risky security cannot be calculated by simply discounting its expected cash flow at the risk-free interest rate. Rather, when a cashflow is risky, to compute its present value we must discount the cashflow we expect on average at a rate that equals the risk-fee interest rate plus an appropriate risk premium.

When cash flows are risky, we can use the Law of One Price to compute present values by constructing a portfolio that produces cash flows with identical risk. Computing prices in this way is equivalent to converting between cash flows today and the expected cash flows received in the future using a discount rate r s that includes a risk premium appropriate for the investment's risk: rs = r + (risk premium for investment s) The investments with higher volatility have rewarded investors with higher average returns. Figure 10.5 is consistent with our view that investors are risk averse. Riskier investments must offer investors higher average returns to compensate them for the extra risk they are taking on. Diversification in Stock Portfolios As the insurance example indicates, the risk of a portfolio of insurance contracts depends on whether the individual risks within it are common or independent. Independent risks are diversified in a large portfolio, whereas common risks are not. consider the implication of this distinction for the risk of stock portfolios. Firm-Specific Versus Systematic Risk Over any given time period, the risk of holding a stock is that the dividends plus the final stock price will be higher or lower than expected, which makes the realized return risky that causes dividends or stock prices, and therefore returns, to be higher or lower than we expect? Usually, stock prices and dividends fluctuate due to two types of news: 1. Firm-specific news is good or bad news about the company itself. For example, a firm might announce that it has been successful in gaining market share within its industry. 2. Market-wide news is news about the economy as a whole and therefore affects all stocks. For instance, the Federal Reserve might announce that it will lower interest rates to boost the economy. Fluctuations of a stock's return that are due to firm-specific news are independent risks. Like theft across homes, these risks are unrelated across stocks. This type of risk is also referred to as firm-specific, idiosyncratic, unique, or diversifiable risk. Fluctuations of a stock's return that are due to market-wide news represent common risk. As with earthquakes, all stocks are affected simultaneously by the news. This type of risk is also called systematic, undiversifiable, or market risk. When we combine many stocks in a large portfolio, the firm-specific risks for each stock will average out and be diversified. Good news will affect some stocks, and bad news will affect others, but the amount of good or bad news overall will be relatively constant. The systematic risk, however, will affect all firms—and therefore the entire portfolio—and will not be diversified. No Arbitrage and the Risk Premium Consider again type I firms, which are affected only by firm-specific risk. Because each individual type I firm is risky, should investors expect to earn a risk premium when investing in type I firms? In a competitive market, the answer is no. To see why, suppose the expected return of type I firms exceeds the risk-free interest rate. Then, by holding a large portfolio of many type I firms, investors

could diversify the firm-specific risk of these firms and earn a return above the risk-free interest rate without taking on any significant risk. The situation just described is very close to an arbitrage opportunity, which investors would find very attractive. They would borrow money at the risk-free interest rate and invest it in a large portfolio of type I firms, which offers a higher return with only a tiny amount of risk. As more investors take advantage of this situation and purchase shares of type I firms, the current share prices for type I firms would rise, lowering their expected return—recall that the current share price Pt is the denominator when computing the stock's return as in Eq. 10.4. This trading would stop only after the return of type I firms equalled the risk-free interest rate. Competition between investors drives the return of type I firms down to the risk-free return. The preceding argument is essentially an application of the Law of One Price: Because a large portfolio of type I firms has no risk, it must earn the risk-free interest rate. This no arbitrage argument suggests the following more general principle: The risk premium for diversifiable risk is zero, so investors are not compensated for holding firm-specific risk. We can apply this principle to all stocks and securities. It implies that the risk premium of a stock is not affected by diversifiable, firm-specific risk. If the diversifiable risk of stocks were compensated with an additional risk premium, then investors could buy the stocks, earn the additional premium, and simultaneously diversify and eliminate the risk. By doing so, investors could earn an additional premium without taking on additional risk. This opportunity to something for nothing would quickly be exploited and eliminated. Because investors can eliminate firm-specific risk "for free" by diversifying their portfolios, they will not require a reward or risk premium for holding it. However, diversification does not reduce systematic risk: Even holding a large portfolio, an investor will be exposed to risks that affect the entire economy and therefore affect all securities. Because investors are risk averse, they will demand a risk premium to hold systematic risk; otherwise they would be better off selling their stocks and investing in risk-free bonds. Because investors can eliminate firm-specific risk for free by diversifying, whereas systematic risk can be eliminated only by sacrificing expected returns, it is a security's systematic risk that the risk premium investors require to hold it. This fact leads to a second key principle: The risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk.

Diversification in Stock Portfolios This principle implies that a stock's volatility, which is a measure of total risk systematic risk plus diversifiable risk), is not especially useful in determining the risk premium that investors will earn. For example, consider again type S and I firms. As calculated in Example 10.6, the volatility of a single type S or 1 firm is 30%. Although both types of firms have the same volatility, type S firms have an expected return of 10% and type I firms have an expected return of 5%. The difference in expected returns derives from the difference in the kind of risk each firm bears. Type I firms have only firm-specific risk, which does not require a risk premium, so the expected return of 5% for type I firms equals the risk-free

interest rate. Type S firms have only systematic risk. Because investors will require compensation for taking on this risk, the expected return of 1 for type S firms provides investors with a 5% risk premium above the risk-free interest rate. We now have an explanation for the second puzzle of Figure 10.6. While volatility might be a reasonable measure of risk for a well-diversified portfolio, it is not an appropriate metric for an individual security. Thus, there should be no clear relationship between volatility and average returns for individual securities. Consequently, to estimate a security's expected return, we need to find a measure of a security's systematic risk. In Chapter 3, we argued that an investment's risk premium depends on how its returns move in relation to the overall economy. In particular, risk-averse investors will demand a premium to invest in securities that will do poorly in bad times (recall, for example, the performance of small stocks in Figure 10.1 during the Great Depression). This idea coincides with the notion of systematic risk we have defined in this chapter. Economy-wide risk—that is, the risk of recessions and booms—is systematic risk that cannot be diversified. Therefore, an asset moves with the economy contains systematic risk and so requires a risk premium....