THE CAPITAL ASSET PRICING MODEL (CAPM) Investment and Valuation of Firms Juan Jose Garcia Machado WS 2012/2013 November 12, 2012 Fanck Leonard Basiliki Loli Blaž Kralj Vasileios Vlachos Contents 1. CAPM............................................................................................................................................... 3 2. Risk and return trade off ............................................................................................................... 4 Risk ................................................................................................................................................... 4 Correlation....................................................................................................................................... 5 Assumptions Underlying the CAPM ............................................................................................. 5 3. Market portfolio .............................................................................................................................. 5 Portfolio Choice in the CAPM World ........................................................................................... 7 4. CAPITAL MARKET LINE ........................................................................................................... 7 Sharpe ratio & Alpha ................................................................................................................... 10 5. SECURITY MARKET LINE .................................................................................................... 10 The Formula .................................................................................................................................. 11 Treynor ratio & Alpha ................................................................................................................. 12 Advantages & Disadvantages of SML........................................................................................ 13 6. BETA .............................................................................................................................................. 13 The Formula .................................................................................................................................. 15 Advantages of Beta ....................................................................................................................... 16 Disadvantages of Beta ................................................................................................................... 16 7. Equilibrium ................................................................................................................................... 17 Definition ....................................................................................................................................... 17 Moving from one market equilibrium to another ...................................................................... 18 Diagrams are a simplification of reality...................................................................................... 18 A Summary of Changes in Market Equilibrium Price ............................................................. 19 8. Difference between Capital Market Line and Security Market Line ...................................... 19 9. Testing Capm ................................................................................................................................ 20 References .......................................................................................................................................... 21 2 1. CAPM The capital asset pricing model, almost always referred to as the CAPM, is a centerpiece of modern financial economics. The model was introduced by Jack Treynor (1961, 1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe, Markowitz and Merton Miller jointly received the Nobel Memorial Prize in Economics for this contribution to the field of financial economics. The model gives us a precise prediction of the relationship that we should observe between the risk of an asset and its expected return. This relationship serves two vital functions. First, it provides a benchmark rate of return for evaluating possible investments. For example, if we are analyzing securities, we might be interested in whether the expected return we forecast for a stock is more or less than its “fair” return given its risk. Second, the model helps us to make an educated guess as to the expected return on assets that have not yet been traded in the marketplace. For example, how do we price an initial public offering of stock? How will a major new investment project affect the return investors require on a company’s stock? Although the CAPM does not fully withstand empirical tests, it is widely used because of the insight it offers and because its accuracy suffices for important applications. In this chapter we first inquire about the process by which the attempts of individual investors to efficiently diversify their portfolios affect market prices. Armed with this insight, we start with the basic version of the CAPM. We also show how some assumptions of the simple version may be relaxed to allow for greater realism. The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf). 3 2. Risk and return trade off Risk, in traditional terms, is viewed as a ‘negative’. The Chinese symbols for risk, reproduced below, give a much better description of risk. The first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity. The principle that potential return rises with an increase in risk. Low levels of uncertainty (low-risk) are associated with low potential returns, whereas high levels of uncertainty (high-risk) are associated with high potential returns. According to the risk-return tradeoff, invested money can render higher profits only if it is subject to the possibility of being lost. Because of the risk-return tradeoff, you must be aware of your personal risk tolerance when choosing investments for your portfolio. Taking on some risk is the price of achieving returns; therefore, if you want to make money, you can't cut out all risk. The goal instead is to find an appropriate balance - one that generates some profit, but still allows you to sleep at night. Measuring return : Risk There are two types of risk: unsystematic risk systematic risk 4 1. What is an unsystematic risk? specific to a firm can be eliminated through diversification examples:-- Safeway and a strike -- Microsoft and antitrust cases 2. What is an systematic risk? market risk cannot be eliminated through diversification due to factors affecting all assets -- energy prices, interest rates, inflation, business cycles Correlation The correlation between two securities falls into one of the following cases: • Positively correlated 0 < ρAB < 1 • Perfectly positively correlated ρAB = 1 • Negatively correlated -1 < ρAB < 0 • Perfectly negatively correlated ρAB = -1 • Uncorrelated ρAB = 0 Assumptions Underlying the CAPM • There are many investors. They behave competitively (pricetakers). • All investors are looking ahead over the same (one period) planning horizon. • All investors have equal access to all securities. • No taxes. • No commissions. • Each investor cares only about ErC and σC. • All investors have the same beliefs about the investment opportunities: rf , Er1,. .,Ern, all σi, and all correlations (“homogeneous beliefs”) for the n risky assets. • Investors can borrow and lend at the one risk free rate. • Investors can short any asset, and hold any fraction of an asset. 3. Market portfolio An investor might choose to invest a proportion of his or her wealth in a portfolio of risky assets with the remainder in cash—earning interest at the risk free rate (or indeed may borrow money to fund his or her purchase of risky assets in which case there is a negative cash weighting). Here, the ratio of risky assets to risk free asset does not determine overall return—this relationship is clearly linear. It is thus possible to achieve a particular return in one of two ways: 1. By investing all of one's wealth in a risky portfolio, 5 2. Or by investing a proportion in a risky portfolio and the remainder in cash (either borrowed or invested). For a given level of return, however, only one of these portfolios will be optimal (in the sense of lowest risk). Since the risk free asset is, by definition, uncorrelated with any other asset, option 2 will generally have the lower variance and hence be the more efficient of the two. This relationship also holds for portfolios along the efficient frontier: a higher return portfolio plus cash is more efficient than a lower return portfolio alone for that lower level of return. For a given risk free rate, there is only one optimal