CFP 502: Module 2. LO 2-1--->2-9: Investment Risk and Return

2-5 Briefly describe covariance, and its importance in constructing a well-diversified portfolio.

*COVARIANCE* measures how much two investments are *related to each other*; in other words, *how much they move together or apart.* In order to diversify we must add an asset that does not behave in the same manner as the asset we already have, otherwise we are just duplicating our current position. The *LOWER* the *COVARIANCE,* the *LOWER* the *CORRELATION* between the two assets, and the more *DIVERSIFICATION* we achieve. As we add additional assets, we want to make sure they are not highly correlated with the assets we already own. *Covariance can be just about ANY NUMBER*, so it can be difficult to understand the correlation. There is a standardized form of covariance that is easier to work with and understand, since it confines the correlation between -1 and +1, and this is called the *CORRELATION coefficient*.

2-9 When constructing a *SYSTEMATICALLY DEVELOPED PORTFOLIO* pay attention to 2 factors.

*Eliminating UNSYSTEMATIC RISK* = BUSINESS AND FINANCIAL *Minimizing TOTAL RISK* (which is measured by *STANDARD DEVIATION*)

2-1 What is *endogenous* risk, and why must advisers be aware of it?

*Endogenous risk* is a risk found *WITHIN* the financial system, and occurs when there is a shock (or panic), which then spreads and is amplified within the system. As advisers saw with the 2008 financial crisis, this type of risk is extremely harmful to investors, and should be taken into account by the adviser when constructing portfolios.

2-7 Assuming that the *CORRELATION (R: -1 TO +1)* of a stock and the market is HIGH, what would BETA coefficient?

*The larger the BETA is, the more VOLATILE the security's historic price is RELATIVE to the MARKET. Investors often use BETA as a rule of thumb for estimating the percentage change in a stock's price when the overall market moves 'X' %. A BETA of 1.0 indicates the movement of the stock would be expected to be identical to the movement of the market. A BETA of .5 means that the price of the stock has been less volatile than the market; for example, if the overall market changes by 4%, the stock would be expected to change by 2%. If a stock has a BETA of 1.5, the price would be expected to change by 6% when the market changes by 4%. Stocks with a HIGH BETA are referred to as "AGGRESSIVE" Stocks with a LOW BETA are referred to as "DEFENSIVE"

2-2 Explain each of the following types of *UNSYSTEMATIC risk* (Can be diversified). 1. *Business risk:* 2. *Financial risk:* 3. *Default risk:* 4. *Credit risk:* 5. *Liquidity and Marketability risk:* 6. *Call risk:* 7. *Event risk:* 8. *Tax risk:* 9. *Investment Manager risk:* 10. *Political risk:*

1. *Business risk:* is related to the uncertainty associated with a particular investment. It most often is concerned with the degree of uncertainty associated with a COMPANY'S earnings and its ability to pay dividends or interest to investors. 2. *Financial risk:* is the risk associated with the degree to which debt is used by a company to finance a particular firm or property. The HIGHER the level of DEBT, the HIGHER the FINANCIAL RISK. An entity with NO DEBT has NO FINANCIAL RISK. 3. *Default risk:* is the chance of the issuer defaulting on its financial obligations, resulting in investors not receiving some or all of their principal. 4. *Credit risk:* is the degree of an issuer's default risk that is reflected in its credit ratings assigned by major credit rating companies. An unanticipated LOWERING of an issuer's DEBT can cause the PRICE of its DEBT to DROP SIGNIFICANTLY in response. 5. *Liquidity and Marketability risk:* LIQUIDITY risk most often is described as the degree of uncertainty associated with the ability to SELL an investment QUICKLY without LOSS OF PRINCIPAL. An alternative definition is the chance of CAPITAL LOSS. MARKETABILITY risk is the risk that there is NO ACTIVE MARKET for an investment. 6. *Call risk:* is the possibility that the issuer will call in the debt issue prior to maturity, resulting in REINVESTING the proceeds at LOWER RATES OF INTEREST. 7. *Event risk:* is the possibility that an unanticipated event or action will affect an issuer's securities in a significant manner. 8. *Tax risk:* is the risk associated with the uncertainty of an adverse outcome due to the interpretation of tax laws and regulations. 9. *Investment Manager risk:* is associated with the actions of the investment manager that could adversely impact one's investment in the fund he or she is managing. 10. *Political risk:* is the uncertainty caused by the possibility of adverse political events occurring in a country.

2-2 Explain each of the following types of *SYSTEMATIC RISK* (Can NOT be diversified away). 1. *Market Risk:* 2. *Interest Rate Risk:* 3. *Reinvestment Risk:* 4. *Purchasing Power Risk:* 5. *Exchange Rate Risk:* P R I M E

1. *Market Risk:* caused by investor reaction to tangible and intangible factors independent of a particular security or property. It is the effect of a movement of the market overall. 2. *Interest Rate Risk:* is the negative effect on the prices of FIXED-INCOME SECURITIES caused by increases in the general level of interest rates. 3. *Reinvestment Risk:* sometimes called reinvestment RATE risk, is the problem of receiving periodic payments or principal and being able to reinvest them only at LOWER RATES. 4. *Purchasing Power Risk:* or INFLATION RISK, is the risk associated with the LOSS OF PURCHASING POWER due to a rise in the general level of prices. 5. *Exchange Rate Risk:* or CURRENCY RISK, is the uncertainty associated with changes in the value of foreign currencies. Relative to the US dollar, it is the risk that converting a foreign currency into US dollars provides fewer dollars than previously held. Purchasing Power Reinvestment Interest Rate Market Exchange Rate Endogenous

2-1 Explain the following terms related to the measurement of investment risk. 1. *Total Risk:* 2. *Standard Deviation:* 3. *Covariance:* 4. *Correlation Coefficient:* 5. *Beta:* A

1. *Total Risk:* The uncertainty that an investment will deliver its expected return; measured by a security's *Standard Deviation.* 2. *Standard Deviation:* The degree to which an investment's returns can be expected to VARY from its mean return. 3. *Covariance:* The tendency of two assets to move together or apart. 4. *Correlation Coefficient:* A standardized version of covariance. 5. *Beta:* A measure of a security's VOLATILITY with respect to an index against which the stock is measured.

2-2 Identify the type of investment risk posed by the following situations. 1. Inflation is expected to rise of the next year. = 2. Exxon Mobil decides to issue bonds instead of stock to finance a new tanker fleet. = 3. The Fed (Reserve: monetaRy policy) decided to increase short-term interest rates to fight increased inflation. = 4. United Airlines fights discount carriers by lowering its fares across the country. = 5. Interest rates have declined over the past year. = 6. The overvalued stock market has finally fallen 15% over the past four months. = 7. The value of your investment in Sony has risen 20% during the past year; during the same period, the yen has weakened against the dollar, causing the total return on the Sony investment to be only 10%. =

1. Inflation is expected to rise of the next year. = Purchasing power risk 2. Exxon Mobil decides to issue bonds instead of stock to finance a new tanker fleet. = Financial risk 3. The Fed (Reserve: monetaRy policy) decided to increase short-term interest rates to fight increased inflation. = Interest rate risk 4. United Airlines fights discount carriers by lowering its fares across the country. = Business risk 5. Interest rates have declined over the past year. = Reinvestment risk 6. The overvalued stock market has finally fallen 15% over the past four months. = Market risk 7. The value of your investment in Sony has risen 20% during the past year; during the same period, the yen has weakened against the dollar, causing the total return on the Sony investment to be only 10%. = Exchange rate risk

2-2 *UNSYSTEMATIC* risk can be DIVERSIFIED away by holding approximately how many securities?

10-15 Large cap securities are required to DIVERSIFY away UNSYSTEMATIC risk.

2-3 Steve Jenkins...20% return on $5,250 and 14% return on $1,750...*Portfolio weight*, weight x return

20 Input 5250 E+ 14 Input 1750E+ Shift, Xw (6 key) = 18.5%

2-4 Calculate the standard deviation, mean return, and coefficient of variation for each stock. Which stock would you choose and why? CV of A CV of B

6 E+ 8 E+ 10 E+ 12 E+ Shift x (7 key) = 9% mean/average return Shift Sx (8 key) = 2.582 CV = St. Dev / Mean = 2.582 / 9.0 = .287 ***Pick stock B because it has a lower CV = less RISK / unit of Return***

2-3 Stargazer fund...mean (average) return of 10%, and a standard deviation of 15%. Assuming the returns are NORMALLY distributed, what range of returns would you expect?

68% of the time = 1 Standard Deviation: 10-15 = -5 and 10+15 = 25 -5% to +25% 95% of the time = 2 Standard Deviations: -5-15 = -20 and 25+15 = 40 99% of the time = 3 Standard Deviations: -20-15 = -35 and 40+15 = 55

2-3 Calculate the standard deviation and mean return for the following individual securities?

8 E+ 10 E+ 12 E+ 14 E+ Shift Sx, Sy (8 key) = Standard Deviation of a Sample = 2.5820 Shift x,y-- (7 key) = Mean return = 11.00

2-7 Answer the following questions about beta. Beta = B = (Si / Sm) x Rim 30 / 15 x 1.0 = 2.0 30 / 15 x .25 = .5 30 / 15 x 0 = 0 30 / 15 x -1 = -2.0 b) What is the significance of *CORRELATION coefficient* to the accurate interpretation of the meaning of *BETA*?

BETA b) Beta is significant if properly calculated. Intuitively, an investor might conclude that a stock with a standard deviation that is twice the standard deviation of the market would have a beta of 2.0. The computations show that to be the case only when the stock in question is highly correlated with the market. Even with a low positive correlation (+.25), the beta is only .5. Many investors will conclude that a stock with a beta of .5 is half as variable as the market What this computation actually tells them is that they *CAN NOT use BETA* to judge the volatility of the stock, but instead must refer to the stock's standard deviation to measure the volatility of the stock. Beta can NOT be accepted blindly without knowing how the stock in question is *CORRELATED* with the market index against which its BETA is calculated.

2-7 What is the approximate *PRICE MOVEMENT* of the following assets, given the following betas, and a market return of +15%? Beta Market Triangle: 1.4 15% W Inc.: -.1 15%

Beta Market Asset Change Triangle: 1.4 x 15% +21% W Inc.: -.1 x 15% -1.5%

2-8 What is the *REQUIRED RETURN = CAPM* for the following securities? The risk-free rate is 4% and the market return is 8%

CAPM = ri = rf + (rm - rf) Bi Triad: = 4 + (8-4) .9 =7.6 Tango: = 4 + (8-4) 1.4 = 9.6

2-4 CV = Coefficient of Variation

CV = Standard Deviation --------------------- Expected Return Unit of Risk ------------ Unit of Return

2-5 Using the data below determine how well stocks B (Std. Dev. = 10.6), C (Std. Dev. = 16.1) and D (Std. Dev. = 23.5) would work with stock A (Std. Dev. = 15.2) in a portfolio. Correlation A/B A/C A/D Coefficient = R = .46 .07 -.13

D has the lowest correlation so it would be best, but B and C are also good options. Coefficient of determination (R^2) = 0-100% = A/B A/C A/D .21 .0049 .0169 The Coefficient of determination (R^2) is quite low for all 3 combos, meaning that very little of the movement of B,C,D can be attributed to the movement of Stock A. In other words, it confirms that each of the three combinations would be good diversifiers and that each of the 3 stocks moves relatively independent of Stock A.

2-9 An investor has an index mutual fund and adds an actively managed fund that has an R2 of .94 with the index fund. Has the investor effectively diversified?

No, the amount of diversification that would be achieved is MINIMAL. 94% of the price movement of the actively managed fund is explained by the index fund. This means that the actively managed fund will essentially mirror the index fund 94% of the time. The investor would be better off looking for a fund that has a lower R2 to the index fund. For DIVERSIFICATION purposes, the LOWER the R2 the BETTER.

2-6 Assume the following securities have the standard deviations and covariances as shown A B C St. Dv. 15.2 10.6 16.1 A/B A/C Covariance +74 +16 Calculate the *CORRELATION coefficient (R)* and the *coefficient of DETERMINATION (R2)*

R = COVij / (Si x Sj) Rab = +74 / 15.2 x 10.6 = .459 Rac = 16 / 15.2 x 16.1 = .065 R2 ab = .4592= 21.2% R2 ab = .0672 = .49%

2-5 The covariance between Twin Pines inc. and the S&P 500 is 95. The standard deviation of Twin Pines Inc. is 13, and the market's standard deviation is 12. What is their correlation (R) coefficient?

R = COVij / SiSj R = 95 / 13 x 12 R = .609

2-5 What does semi-variance measure?

Semi-variance measures only the returns that fall below the average, and is primarily used by portfolio managers. It recognizes that investors are concerned less about upside potential and more about downside risk.

2-6 What does the *coefficient of DETERMINATION (R2)* tell us about *SYSTEMATIC AND UNSYSTEMATIC* risk?

The *coefficient of DETERMINATION (R2)* tells us how much of the risk is explained by the benchmark. For example, if we are comparing the Titanic Fund to the S&P 500 and the coefficient of determination is .7, this would mean that 70% of the price movement of the Titanic Fund is explained by the S&P 500 (Market SYSTEM/ Benchmark = SYSTEMATIC risk), and the other 30% is not explained by the S&P 500 Index (UNsystematic risk = business = individual stock/fund). For *DIVERSIFICATION* purposes, the LOWER the *coefficient of DETERMINATION (R2)* (and thus *CORRELATION coefficient*) the *BETTER*. However *beta* is a measure of *SYSTEMATIC RISK* and since the *coefficient of DETERMINATION (R2)* is a measure of systematic risk, when using *beta* the HIGHER the *coefficient of DETERMINATION (R2)* the BETTER

2-3 Libra...has a mean return of 11% and a standard deviation of 9. Assume normal distribution, what is the probability that the stock will have a return greater than 20%?

The answer is 16%. We know that half of the returns are going to be greater than the mean return of 11%. We also know that one standard deviation (which will be evenly distributed) accounts for 68% of the returns and would range from +2 to +20%. Half of the 68% of returns would be above the mean return, and half below. So 34% of the returns would be greater than the 11% mean return, and would fall between 11% and 20%. If we know 50% of the returns will be greater than 11%, and we know that 34% of the returns will fall between 11% and 20%, we then know that 16% (50-34 = 16%) of the returns will be greater than 20%.

2-3 Scorpio...has a mean return of 19% and a standard deviation of 25. What is the probability that the stock will have a return greater than 19% if the returns are normally distributed?

The answer is 50%. In a normally distributed yield curve, half of the returns will be greater than the mean return, and half will be less than the mean return.

2-8 What is the long-term historical market risk premium in the US?

The long-term historical market risk premium in US, from 1926-2015 has been 6.6% Market risk premium = Rm =Rf = 10-3.4 = 6.6%

2-8 What is the appropriate TREASURY SECURITY to use for the RISK FREE RATE?

The most widely used TREASURY SECURITY is the *THREE-MONTH TREASURY BILL*, and this is what is favored by the CFP Board for the exam. However, some portfolio managers use the 5-year or 10-year Treasury NOTE since stocks are a LONG-term investment, and the investor's holding period is often 5-10 years or longer.

2-8 What is the term used for the difference between the market return and the risk-free rate (Rm - Rf)?

This is called the *"Market Risk Premium"*. It is the excess return earned above the risk-free rate to COMPENSATE the investor for taking EXTRA RISK by INVESTING in the MARKET. There is much discussion and disagreement over what the future market risk premium will be.

2-6 Stock F: 9% return, 7 Std. Dev. Stock G: 14% return, 16 Std. Dev. Covariance: COV = -22 a) Expected return of a portfolio that has 40% in F and 60% in G. b) What is the standard deviation of a portfolio containing these 2 stocks? Sp = SqRt of {Wf^2Sf^2 + Wg^2Sg^2 + 2WfWgCOVfg} c) What are the *CORRELATION coefficient* and the *coefficient of DETERMINATION* of stock F and G?

a) .4x9 = 2.6 .6x14 = 8.4 3.6%+8.4% = 12% b) Sp = SqRt of {(.4)^2(7)^2 + (.6)^2(16)^2 + 2(.4)(.6)(-22) = 9.5 c) Rfg = R = - 22 / (7 x 16) = -.2 R^2 = .04

2-3 Weighted Average Return Weighted Beta Walter... a) 1st: Weighted-Average expected return b) 2nd: Multiply weight x beta = weighted beta coefficient i) .625 x .15 = .0938 + .375 x .10 = .0375 =.1313 = 13.13% OR a) Weighted average expected return b) Weighted beta ***c) What would happen to the overall level of risk?***

a) 15 Input 50,000 E+ 10 Input 30,000 E+ Shift Xw (6 key) = .13125 = 13.125% b) 1.3 Input 50,000 E+ .7 Input 30,000 E+ Shift Xw (6 key) = 1.075 c) The overall level of risk for Walter's portfolio would rise because the beta increases from 1.0750 for the old portfolio to 1.2250 for the new portfolio. [[ A HIGHER BETA is more risk...and *POSSIBILITY* of more return]]