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## CHAPTER 8 Risk and Rates of Return

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**CHAPTER 8Risk and Rates of Return**Investor like return but dislike risk, thus they invest in risky asset only if they expect to receive higher returns. All financial assets are expected to produce CF. Thus the riskiness of an asset is based on the riskiness of its CF The riskiness of an assets classified in to : Stand-alone risk Portfolio risk**Investment returns**• Business or individual invest money today with the expectation of earning even more money in the future. • The concepts of return – expressing the financial performances of an investment • The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = ________________________ Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.**RETURN**Expected Return ( k )- the return that an investor expects to earn on an asset, given its price, growth potential, etc. Required Return ( k )- the return that an investor requires on an asset given itsrisk and market interest rates.**For a Treasury security, what is the required rate of**return? Risk-free rate of return Required rate of return = Since Treasury’s are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return.**For a corporate stock or bond, what is the required rate of**return? Risk-free rate of return Required rate of return Risk Premium = + • How large of a risk premium should we require to buy a corporate security? • Risk premium – the portion of the expected return that can be attributed to the additional risk of an investment**Calculate the Expected Rate of Return**• The weighted average of the outcomes where the weight are probabilities. • The rate of return expected to be realized from an investment. (the return that an investor expects to earn on an asset, given its price, growth potential.) Expected rate of return= P1k1 + P2k2+….Pnkn = Piki**Expected Return**State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% For each firm, the expected return on the stock is just a weighted average:**Expected Return**State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% For each firm, the expected return on the stock is just a weighted average: k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn**Expected Return**State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn k (OU)= .2 (4%)+ .5 (10%)+.3 (14%) = 10% k (OI) =.2 (-10%)+ .5 (14%) + .3 (30%) = 14%**Based only on your expected return calculations, which stock**would you prefer?**Have you considered**RISK?**What is investment risk?**• The possibility that an actual return will differ from our expected return(the variability in return or outcomes from the investment) • The greater the chance of lower than expected or negative returns, the riskier the investment. • Two types of investment risk • Stand-alone risk • Portfolio risk**Company A**Company B return return Thus what is the risk? • Uncertainty in the distribution of possible outcomes.(Probability of Occurrence)**Probability distributions ?**A listing of all possible outcomes, and the probability of each occurrence. The tighter the probability distribution, the less its variability. Most likely the actual rate of return is close to the expected rate of return. Thus,the tighter the probability distribution the lower the risk associated to a stock Thus, Standard Deviation is one measure of risk.**Firm X**Firm Y Rate of Return (%) -70 0 15 100 Expected Rate of Return Probability Distribution**How do we Measure Risk?**• A more scientific approach is to examine the risk of security is using STANDARD DEVIATION of returns. • Standard deviation is a measure of the dispersion of possible outcomes. Expected rate of return (k)= Piki Deviation = ki - k**How do we Measure Risk?**Standard deviation (σi) measures total, or stand-alone, risk. The greater the standard deviation, the greater the uncertainty,and therefore , the greater the RISK. (the lower the probability that actual returns will be closer to expected returns.) Larger σi is associated with a wider probability distribution of returns. Difficult to compare standard deviations, because return has not been accounted for.**s**n i=1 S 2 = (ki - k) P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 = 3.46%**s**n i=1 S 2 = (ki - k) P(ki) Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 (14% - 14%)2 (.5) = 0 (30% - 14%)2 (.3) = 76.8 Variance = 192 Stand. dev. = 192 = 13.86%**Which stock would you prefer?**How would you decide?**Which stock would you prefer?**How would you decide? Easy to choose between 2 investment that have the same risk but different expected return. Prefer the higher expected return. Similarly, easy to choose between 2 investment that have the same expected return but different risk. Prefer the lower risk (standard deviation) However if given 2 investment to choose have different risk and expected return have to use another measurement.**Coefficient of Variation (CV)1 unit of Return = ? Risk**• A standardized measure of dispersion about the expected value, that shows the risk per unit of return. • It provide more meaningful basis for comparison when the expected return on two or more alternative are not the same • It is useful when considering investment when have different expected rates of return and different level of risk. *The larger the CV, the greater the risk**Prob.**A B Rate of Return (%) 0 Illustrating the CV as a measure of relative risk σA = σB , but A is riskier because of a larger probability of losses. In other words, the same amount of risk (as measured by σ) for less returns.**Summary**Orlando Orlando Utility Technology Expected Return 10% 14% Standard Deviation 3.46% 13.86% CV 0.346 0.99 Know as stand alone risk**Why is the T-bill return independent of the economy? Do**T-bills promise a completely risk-free return? T-bills will return the promised 8%, regardless of the economy. No, T-bills do not provide a risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time. T-bills are also risky in terms of reinvestment rate risk. T-bills are risk-free in the default sense of the word.**Investor attitude towards risk**• Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. • Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities. • Implication of Risk averse for security price and rate of return- the higher a security risk, the lower its price and the higher its required return**Stock B is more risky than stock A**If investor is risk averse, the new investor will buy stock A. Simultaneously, B stockholder start to sell it stock and buy stock A (with the money they get from selling stock B) Buying pressure would drive up the price of stock A, while selling pressure would cause the stock B price decline Change in price, cause the change in expected return of the 2 security. If the stock B Price decline to $75, ($15/$75) the K=20%, whereas the stock A price rise to $150, ($15/150) the k=10% (formula ks = D/P) 20%-10% = 10% - risk premium(compensation to investor for the additional risk) B- risky, lower price (decline) &higher K=20% Stock A Stock B Rate of Return (%) -70 0 15 100 Expected Rate of Return Investor attitude towards risk-Both stock P=$100 & K=15%**RISK &DIVERSIFICATION**• Risk of an investment can be reduce through diversification of investments across diff securities rather than invest in only one stock, (i.e investing in more than one security in order to reduce the total risk.) • How does this work? • by combining several securities in a portfolio. • Total risk can be minimized by investing in combining securities(portfolio) that NOT perfectly correlated. i.e an asset with a negative correlation**PORTFOLIO**• Reduction in risk through diversification by investing in different type of assets (portfolio). • Portfolio– Hold/Invest in a collection /combination of different types of assets /investments at the same time or period • E.g: If you owned TNB stock, some Renong stock and some Hicom sock, you would holding a three-stock in a portfolio. • Portfolio:- • Expected return is the weighted average of the expected return on the individual assets in the portfolio • Risk is NOT the weighted average of the standard deviation of the individual assets in the portfolio. However the portfolio is smaller than the weighted average of the assets standard deviation**Calculating portfolio expected return:Weighted average of**the expected return on the individual assets in the portfolio You formed a $100,000 portfolio, investing $25,000 in each stock Stock Ex. Return TNB 12.0% Telekom 11.5% Petronas 10.5% Shell 9.5%**DIVERSIFICATION- Reduce the Risk**• How does the risk can be reduce by holding portfolio? • Invest in different type of securities may lower the risk of losses. This is because, if we loss in security A, probably, for security B we will earn profit. • To reduce a risk from our portfolio depends on the correlation (r) between all of the stocks. • If two stocks are perfectly positively correlated, diversification has NO effect on risk. i.e If correlation (r) = 1, we cannot eliminate all the risk. • If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified. i.e If correlation (r) = -1, we can eliminate the risk • If correlation (r) = -1< r < 1, we can reduce the risk involved.**Is all the Risk can be Eliminated ?**• Investors should NOTexpect to eliminate all risks from their portfolio- Some risk can be diversified away and some cannot. • Total Risk() – Unsystematic Risk + Systematic risk • Market risk –Risiko Pasaran (systematic risk) is non diversifiable. This type of risk cannot be diversified away. • Company-unique risk-Risiko Unik(unsystematic risk) is diversifiable. This type of risk can be reduced through diversification.**Market Risk (Systematic Risk)**• This is non-diversifiable risk because it is beyond the control of the investor and the firm. • Market risk is measured by beta which is equivalent to 1.0. • For Example :- • Unexpected changes in interest rates. • Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.**Firm-Specific (Unique) Risk/Unsystematic Risk**• This risk can be reduced or eliminated through investment diversification. • A company’s labor force goes on strike. • A company’s top management dies in a plane crash. • A huge oil tank bursts and floods a company’s production area.**As you add stocks to your portfolio, firm-specific risk is**reduced. portfolio risk Firm- specific risk Market risk number of stocks**Risk and Diversification**• Conclusion: The market rewards diversification. By diversifying our investments, we can lower risk without sacrificing expected return, or we can increase expected return without having to assume more risk.**Do some firms have more market risk than others?**Yes. For example: Interest rate changes affect all firms, but which would be more affected: a) Retail food chain b) Commercial bank**Note**• As we know, the market compensates investors for accepting risk - but only for market risk. Firm-specific risk can and should be diversified away. • So - we need to be able to measure market risk.**This is why we have BETA.**What is Beta(): a • Specifically, it is a measure of how an individual stock’s returns vary with market returns. • It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market. • Eg: β = 1.4 means any increase/decrease by 1% in market return will cause an increase or decrease by 1.4% in asset return**The market’s beta is 1**• A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market. • A firm with a beta > 1 is more volatile than the market (ex: computer firms). • A firm with a beta < 1 is less volatile than the market (ex: utilities). • Most stocks have betas between 0.60 and 1.60**Measuring Market Risk**• Market portfolio refer to the combination of investments including risky assets which are available in the market. • However, it is complex to create a portfolio that consist of all assets in the market together its return.**Measuring Market Risk**• Thus, proxy can be used as a market portfolio such as S&P 500 Index in USA and Nikkei 225 Index in Japan • In Malaysia, KLCI and Emas Index are some of the proxies that can be used as market portfolio • The movement in these indexes act as a benchmark to the movement of the market**Market Portfolio Returns**• Market returns and assets returns for certain period can be determined by looking at the percentage of changes in index or price indeks (harga pada tempoh tersebut melalui persamaan berikut: kt = 1 Pt dimana; kt = pul bg suatu tempoh pegangan t bg sykt atau portfolio pasaran. Pt = harga saham (atau indeks psrn) pada tempoh t Pt = harga saham (atau indeks psrn) pada tempoh t -1 Pt - 1**Asset Return & Market Return**AssetMarket Period Price Return Index Return 0 19.00 853.42 1 19.29 1.53% 869.10 1.84% 2 20.90 8.34%* 900.67 3.63% 3 19.54 -6.51% 901.890.14%* 4 21.50 10.03% 923.80 2.42%**Measuring Market Risk**• Once the asset return and market return obtained, a graph is prepare to see the r/ship between asset return and market return. • Asset return is plot on Y-axis and market return on X-axis. • When all the returns are plotted, draw a line of best-fit through coordinate point (0,0), which we call Characteristic line. • The slope of the line (beta), represents the average movement of the firm’s stock returns in response to a movement in the market’s return i.e the average relationship between a stock’s return and market’s returns**Calculating Beta**15 10 5 -15 -10 5 15 -5 10 -5 -10 -15 XYZ Co. returns Market (S&P 500) returns**Calculating Beta**15 10 5 -15 -10 5 15 -5 10 -5 -10 -15 Beta = slope = 1.20 XYZ Co. returns . . . . . . . . . . . . . . . . . . . . . . . S&P 500 returns . . . . . . . . . . . . . . . . . . . .**β Portfolio Measurement**• Portfolio beta-the relationship between a portfolio’s returns and the market ‘s returns. • It is a measure of the portfolio’s nondiversifiable risk. i.e the average of the individual stocks betas. • Actually, it is a weighted average of the individual securities betas, the weight being equal to the proportion of the portfolio invested in each security.**β Portfolio Measurement**• An asset portfolio is a combination of an individual assets and each asset has its own beta. • The portfolio beta is a weighted average of the individual assets’ beta. • Portfolio beta is derive from the following equation: βp = ∑ wj βj n J = 1**Interpretation of portfolio beta.**βp = 1.3 • Eg: , whenever the general market increase or decrease 1 percent, the portfolio’s return would on average change 1.3 percent. • β is the underlying basis often used for measuring a security’s or portfolio’s risk. • It is useful to financial manager to specify the relationship should be between an investor’s required rate of return and the stock’s or portfolio’s risk-market risk.

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