Financial Management Liliya N. Zhilina, World Economy and Inrernational Relations Department, Vladivostok State University of Economic and Services (VSUES). 4. Risk and Return. CAPM-model.

Investment Return Investment returns measure the financial results of an investment. Returns may be historical or prospective (anticipated). Returns can be expressed in:  Money terms:  Percentage terms: $ Received - $ Invested $1,100 - $1,000 = $100 ($ Received – Invested) / $ Invested $100 / $1,000 = 0.10 = 10%

Cost (Price) of Debt Capital: Cost of Equity: Required Dividend Capital Return Return Gain = + Interest Rate

Factors affect the cost of capital Production opportunities (returns, which a producer expects to earn, makes the upper limit of the payment for capital) Market conditions, especially interest rates and tax rates. Time preferences for consumption / savings The firm’s investment policy. Firms with riskier business-projects generally have a higher cost of capital. The firm’s capital structure and dividend policy. Expected inflation (the higher risk - the expensive capital)

k = k* + IP + DRP + LP + MRP = k RF +DRP + LP + MRP Here: k = Required rate of return on a debt security. k* = Real risk-free rate. k RF = Nominal risk-free rate. IP = Inflation premium. DRP = Default risk premium. LP= Liquidity premium. MRP = Maturity risk premium. Factors Influence Interest Rates

Premiums Added to k* for Different Types of Debt Sort-Term Treasury (governmental): only IP for ST inflation Long-Term Treasury (governmental): IP for LT inflation, MRP Sort-Term corporate: ST IP, DRP, LP Long-Term corporate: IP, DRP, MRP, LP

More Factors Influence Interest Rates The Central Bank Policy (money supply – commercial banks crediting). Deficit (shortfall) / surplus of the budget. Trade balance. Interest rates in other countries.

Risks Investing Abroad Country Risk: depends on economy conditions, political and social factors in a country. Exchange Rate Risk: if investments (securities) have been nominated in a national currency the investments cost depends on exchange rate. Exchange rate change depends on: changing in a relative inflation; increase in a country risk leads to drop of national currency rate.

Risk Can be defined as the chance that some unfavorable event will occur.

What is investment risk? Typically, investment returns are not known with certainty. Investment risk pertains to the probability of earning a return less than that expected. The greater the chance of a return far below the expected return, the greater the risk.

How can be considered the risk of investing in some asset? 1) on a stand-alone basis (each asset by itself); 2) In a portfolio context, where the investment is combined with other assets and its risk is reduced through diversification. Stand-alone risks: compare risks of purchasing а) short-term governmental bills with an expected return of 5 %; and б) shares of just being organized company that plans to start drilling in a new oil field with an expected return from % to –100 %.

Probability distribution of returns of the stocks H and L Demand Probability, P Return on the stocks, k HL High0,3100%20% Average0,415% Low0,3-70%10% Total1,0

Average return (k): gains matrix Demand P Stock НStock L ReturnTotalReturnTotal High0,3100%0,3*100=30%20%0,3*20=60% Average0,415%0,4*15=6%15%0,4*15=6% Low0,3-70%0,3*-70=-21%10%0,3*10=3% Total1,0 k=15%

Probability distribution Rate of return (%) Stock L Stock H Which stock is riskier? Why?

Standard deviation measures the stand-alone risk of an investment. The larger the standard deviation, the higher the probability that returns will be far below the expected return. Coefficient of variation is an alternative measure of stand-alone risk.

The standard deviation, : Variance     Expected rate of return, k : Coefficient of variation (risk per unit of return). CV = / k Measures of Risk Formulas: ^ ^  2   ^ k

Risks and Returns of the stocks H & L  = (( ) (15-15) ( ) 2 0.3) 1/2 = 65,84%.  = (( ) (15-15) (10-15) 2 0.3) 1/2 =3,87%. Н L Stock Expected rate of return Standard deviation Coefficient of variation H15%65,84%4,39 L15%3,87%0,26 The stock Н is 17 times risky than the stock L

Probability Ranges for a Normal (Gaussian ) Distribution 99,74% k 95,46% 68,26% -1σ +1σ -2σ-3σ +2σ+3σ Probabilities that returns would be in the intervals ±1 SD, ±2 SD, ±3SD

Risk-averse investors The average investor is risk-averse (dislikes risk), which means that he or she must be compensated for holding risky assets. At the market, where most investors are risk-averse, riskier assets have higher required returns than less risky assets.

Portfolio risk An asset is stored in a stock portfolio could be considered less risky than stored alone. The portfolio (diversification) provides average return but much lower risk. The key here is negative correlation. Correlation is the tendency of two variables to move together. Expected return of a portfolio is the weighted average of expected returns of separate assets: k p = w 1 k 1 + w 2 k 2 + …. w n k n = ∑w i k i i=1 n

Two stocks can be combined to form a riskless portfolio if r = Risk is not reduced at all if the two stocks have r = In general, stocks have r  0.65, so risk is lowered but not eliminated. Investors typically hold many stocks. What happens when? r = 0 suggests that the two variables are not related to one another; that is, they are independent. r – correlation coefficient Two-Stock Portfolios

What would happen to the risk of an average few-stock portfolio as more randomly selected stocks were added?  p would decrease because the added stocks would not be perfectly correlated, but k p would remain relatively constant.

# Stocks in Portfolio Company Specific (Diversifiable) Risk Market Risk 20,1 0 Stand-Alone Risk,  p  p (%) 35 Amount of a Portfolio Stock and its Risk The market portfolio is a portfolio consisting of all stocks. Its SD ≈ 20,1%

Stand-alone Market Diversifiable Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification. risk risk risk = +

As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.  p falls very slowly after about 40 stocks are included. The lowest limit for  p is about 20,1% =  M. Rational investors will minimize risk by holding portfolios. They bear only market risk, so prices and returns reflect this lower risk. By forming well-diversified portfolios, investors can eliminate about half the riskiness of owning a single stock.

Сapital Аsset Рricing Мodel (CAPM). By William Sharp and othrers. CAPM is the equilibrium model, which sets up dependence between risk and required return for assets (shares) in the well diversified portfolio. The assumption of CAPM. Risk has one influence factor: a stock volatility relative to the market. The relevant risk of an individual stock, which is called its beta coefficient, is defined under the CAPM as the amount of risk that the stock contributes to the market (well-diversified) portfolio. How should the risk of an individual stock be measured?

How are betas calculated? Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis. The stock’s beta coefficient ( b i or β) is equal to the slope angle v of the regression line, which measures relative volatility: β i = b i = (σ i / σ M )* r i M here: r i M – the correlation between the i’th stock’s expected return and the expected return on the market; σ i, σ M – the standard deviations of the i’th stock’s expected return and the expected return on the market

Use the historical stock returns to calculate the beta for the stock of Y (MD). YearsMarketY 1 25,7%40,0% 2 13,0%-35,0% 3 -8,2%-25,0% 4 25,0%45,0% 5 22,5%10,0% 6 15,7%15,0% 7 40,0%46,0% 8 12,0%-25,0% 9 -5,8%25,0% 10 -9,1%-24,0%

Calculating Beta for Y ( MicroDrive) k M

How is beta calculated? The regression line, and hence beta, can be found using a spreadsheet program. In this example, b = Analysts typically use four or five years’ of monthly returns to establish the regression line. Some use 52 weeks of weekly returns. The R 2 measures the percent of a stock’s variance that is explained by the market. The typical R 2 is: –0.3 for an individual stock –over 0.9 for a well diversified portfolio

How is beta interpreted? If b = 1.0, stock has average (of the broader market) risk. If b > 1.0, stock is riskier than average. If b < 1.0, stock is less risky than average. Most stocks have betas in the range of 0.5 to 1.5. Theoretically, it is possible for a stock to have a negative beta: when the stock’s return would tend to rise whenever the returns on other stocks fall. Value Line (valueline.com)

Expected Return versus Market Risk Expected SecurityreturnRisk, b HighTech. 17.4% 1.29 Market Utilities T-bills Collections Which of the alternatives is best?

Use the SML to calculate each alternative’s required return The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM). SML: k i = k RF + (RP M )b i k RF – risk free return, k M – market return. Assume k RF = 8%; k M = k M = 15%. RP M = (k M - k RF ) = risk premium = 15% - 8% = 7%. ^

Required Rates of Return k HT = 8.0% + (7%)(1.29) = 8.0% + 9.0%= 17.0%. k M = 8.0% + (7%)(1.00)= 15.0%. k Ut = 8.0% + (7%)(0.68)= 12.8%. k T-bill = 8.0% + (7%)(0.00)= 8.0%. k Coll = 8.0% + (7%)(-0.86)= 2.0%.

Expected versus Required Returns ^ k(exp.)k (req.) HT 17.4% 17.0% Undervalued Market 15.0 Fairly valued Ut Undervalued T-bills 8.0 Fairly valued Coll Overvalued

.. Coll.. HT T-bills. Ut k M = 15 k RF = SML: k i = k RF + (RP M ) b i k i = 8% + (7%) b i k i (%) Risk, b i SML and Investment Alternatives Market The slope of the SML equation is ( k M - k RF), the market risk premium.

Limitation of the CAPM The CAPM is a single factor model. Richard Roll showed that it is virtually impossible to prove investors behave in accordance with CAPM theory. CAPM/SML concepts are based on expectations, yet betas are calculated using historical data. A company’s historical data may not reflect investors’ expectations about future riskiness. Betas of individual securities are not good estimators of future risk. Betas of portfolios of 10 or more randomly selected stocks are reasonably stable. Past portfolio betas are good estimates of future portfolio volatility.