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FIN 302 Lecture Notes - Lecture 19: Squared Deviations From The Mean, Expected Return, Standard Deviation

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goldfox765
17 Mar 2019
School
U of M
Department
Finance
Course
FIN 302
Professor
Qin Lei

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18

FIN 302 Lecture Notes - Lecture 18: Squared Deviations From The Mean, Dividend Yield, Capital Market

19

FIN 302 Lecture Notes - Lecture 19: Squared Deviations From The Mean, Expected Return, Standard Deviation

20

FIN 302 Lecture Notes - Lecture 20: Total Return, Expected Return

Document Summary

Excepted returns are based probabilities of possible outcomes. Variance and standard deviation: measures volatility of returns, unequal probabilities for entire range, variance is weighed of squared deviations. An asset risk and return is important to determine the ror of the whole portfolio. The risk return tradeoff is measured by portfolio expected return and stdv. Portfolio return may not as high as best performer, and may not be as low as the individual worst performer. The expected return for the portfolio is the weight average returns for each asset in the portfolio. Expected return can be calculate by find return in each possible state and compute the expected value. Using same formula as for the individual asset. Variance and stdv can also using the same formulas. Total return = expected return + unexpected return. Unexpected return = systematic portion + unsystematic portion. Total return = expected return + systematic portion + unsystematic portion.

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Related Questions

Hi guys could someone help me and explain in detail the two fundamental principles of investments – the risk/return tradeoff and diversification. Also, describe how asset allocation and the correlation of various securities within asset classes impact the riskiness of an investor’s portfolio.

I found an answer but it seems to me very long and not sure about it so can you help me out guys

ANS:

Risk /Return Tradeoff

Risk, return and liquidity are three dimensions of investment decision. Risk/Return trade off considers two dimension ie risk and return. As risk of an investment increases , its expected return will decrease. Risk is measured by volatility of return which can be statistically obtained by standard deviation of return. Higher the standard deviation, higher will be volatility of return and higher the risk

Risk can be also measured as a relative risk compared to the market. This is measured by stock beta with reference to a market index. Higher the beta, higher the value of stock Beta, higher will be the risk .

Investors seeking higher return will need to take higher risks.

Treasury bonds are almost risk free assets. This has the lowest rate of return. Stocks have higher risk , hence have higher expected return. High beta stocks will have higher risk and higher returns.

An investor should understand his risk taking ability and will have to make a trade off between risk and return depending on his risk apetite.

Diversification:

There is a saying, do not put all your eggs in one basket. The reason is that it has higher risk if all eggs are in one basket. If the eggs are distributed in different basket, risk of loss decreases.

Same principle is applied in investment. Diversification reduces risk.

If one invests in different classes of assets like bonds, stock, commodities and properties –his risk is likely to reduce. Reduction in return in one asset is likely to be compensated by return in other asset.

Within one class of asset also, there should be diversification to reduce risk.

For example one stock “A “may have expected return of 10% and standard deviation of 5%.This risk can be reduced by diversification in number of assets and the ratio of Risk/return can be decreased.

If we diversify and instead of investing 100% in stock A, we invest 60% in “A” and 40% in another stock “B” having expected return15% and standard deviation of 8%.assume the correlation between the two assets are 0.5

Portfolio return=wa*Ra+wb*Rb

Wa=Weight of asset A=0.6

Wb=Weight of asset B=0.4

Ra=Return of A=10%

Rb=Return of B=15%

Sa=Standard deviation of A=5%

Sb=Standard deviation of B=8%

Corr(a,b)=Correlation of A & B=0.2

Portfolio return=0.6*10+0.4*15=12%

Portfolio Variance=(wa^2)*(Sa^2)+(wb^2)*(Sb^2)+2wa*wb*Cov(a,b)

Cov(a,b)=Corr(a,b)*Sa*Sb=0.1*5*8=4

Portfolio Variance=(0.6^2)*(5^2)+(0.4^2)*(8^2)+2*0.6*0.8*4=23.08

Portfolio standard deviation=Square root of Variance=(23.08^0.5)=4.8%

The diversification has increased return and reduced risk

Stock A was giving 10% return with 5% standard deviation. With diversification of portfolio we have 12% return and 4.8% standard deviation. Risk return ratio is decreased.

It may be noted that, higher the correlation between assets in the portfolio, higher will be risk in terms of standard deviation. Hence it is better to diversify with uncorrelated assets.

Diversification reduces unsystematic risk,but it cannot reduce systematic risk of overall market or economy

Fill in the blank using a number of terms listed below (@1 point per question).

Beta coefficient, Bonds, CAPM, Cash flows, Change, CV, Convertible bonds, Correlation, Correlation coefficient, Debenture, Discount, Diversifiable risk, Expected return, Interest rate risk, Inverted, Junk Bonds, Market risk, More, Normal, Opposite, Probability distribution, Ratings, Reinvestment rate risk, Risk, Risk averse investor, Risk premium, Standard deviation

______________is the chance that some unfavorable event will occur. For instance, the risk of an asset is essentially the chance that the asset’s cash flows will be unfavorable or less than expected.

A __________________ is a listing, chart or graph of all possible outcomes, such as expected rates of return, with a probability assigned to each outcome.

The ______________________is a statistical measure of the variability of a set of observations. The variance of the probability distribution is the sum of the squared deviations about the expected value adjusted for deviation.

The _______________________ is equal to the standard deviation divided by the expected return; it is a standardized risk measure which allows comparisons between investments having different expected returns and standard deviations.

A _______________________ dislikes risk and requires a higher rate of return as an inducement to buy riskier securities. A realized return is the actual return an investor receives on their investment. It can be quite different than their _______________________.

A ________________ is the difference between the rate of return on a risk-free asset and the expected return on Stock i which has higher risk.

_________________ is a model based upon the proposition that any stock’s required rate ofreturn is equal to the risk free rate of return plus a risk premium reflecting onl y the risk remaining after diversification.

_________________ is the tendency of two variables to move together. A _________________ of +1.0 means that the two variables move up and down in perfect synchronization, while a coefficient of -1.0 means the variables always move in opposite directions.

_________________ is that part of a security’s total risk that cannot be eliminated by diversification. It is measured by the beta coefficient. _________________ is also known as company specific risk. This risk can be eliminated by proper diversification.

The _________________ is a measure of a stock’s market risk, or the extent to which the returns on a given stock move with the stock market.

Instructions: Use the formula below to compute the problems: “Please Read the question carefully.”

Kd = Yield (1 – T)

1. Telecom Systems can issue debt yielding 8 percent. The company is in a 35 percent bracket. What is its after-tax cost of debt?

2. After-tax cost of debt: Royal Jewelers Inc., has an aftertax cost of debt of 6 percent. With a tax rate of 40 percent, what can you assume the yield on the debt is?

3.

Cash flow: Assume a corporation has earnings before depreciation and taxes of $100,000, depreciation of $50,000, and that it has a 30 percent tax bracket. Compute its cash flow using the format below.

Earnings before depreciation and taxes _____

Depreciation _____

Earnings before taxes _____

Taxes @ 30% _____

Earnings after taxes _____

Depreciation _____

4.

Cost of preferred stock: Medco Corporation can sell preferred stock for $80 with an estimated flotation cost of $3. It is anticipated the preferred stock will pay $6 per share in dividends.

a. Compute the cost of preferred stock for Medco Corp.

b. Do we need to make a tax adjustment for the issuing firm?

5. Cost of preferred stock: The Meredith Corporation issued $100 par value preferred stock 10 years ago. The stock provided an 8 percent yield at the time of issue. The preferred stock is now selling for $75. What is the current yield or cost of the preferred stock? (Disregard flotation costs.)

6. Costs of retained earnings and new common stock: Barton Electronics wants you to calculate its cost of common stock. During the next 12 months, the company expects to pay dividends (D1) of $1.20 per share, and the current price of its common stock is $30 per share. The expected growth rate is 9 percent.

a. Compute the cost of retained earnings (Ke). Use Formula 11-6.

b. If a $2 flotation cost is involved, compute the cost of new common stock (Kn). Use Formula 11-7.

7. A firm's cost of preferred stock is equal to the preferred dividend divided by market price plus the dividend growth rate (Kp= D/Po+ g).

8. The coefficient of variation, calculated as the standard deviation of expected returns divided by the expected return, is a standardized measure of the risk per unit of expected return.

a. True

b. False

9. The standard deviation is a better measure of risk than the coefficient of variation if the expected returns of the securities being compared differ significantly.

a. True

b. False

10. The CAPM is built on historic conditions, although in most cases we use expected future data in applying it. Because betas used in the CAPM are calculated using expected future data, they are not subject to changes in future volatility. This is one of the strengths of the CAPM.

a. True

b. False

11. You have the following data on three stocks:

Stock

Standard Deviation

Beta

A

20%

0.59

B

10%

0.61

C

12%

1.29

If you are a strict risk minimizer, you would choose Stock if it is to be held in isolation and Stock if it is to be held as part of a well-diversified portfolio.

a. A; A.

b. A; B.

c. B; A.

d. C; A.

e. C; B.

12. A portfolio’s risk is measured by the weighted average of the standard deviations of the securities in the portfolio. It is this aspect of portfolios that allows investors to combine stocks and thus reduce the riskiness of their portfolios.

a. True

b. False

13. You are considering two bonds. Bond A has a 9% annual coupon while Bond B has a 6% annual coupon. Both bonds have a 7% yield to maturity, and the YTM is expected to remain constant. Which of the following statements is CORRECT?

a. The price of Bond B will decrease over time, but the price of Bond A will increase over time.

b. The prices of both bonds will remain unchanged.

c. The price of Bond A will decrease over time, but the price of Bond B will increase over time.

d. The prices of both bonds will increase by 7% per year.

e. The prices of both bonds will increase over time, but the price of Bond A will increase at a faster rate.

14. A 12-year bond has an annual coupon of 9%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 7%. Which of the following statements is CORRECT?

a. If market interest rates decline, the price of the bond will also decline.

b. The bond is currently selling at a price below its par value.

c. If market interest rates remain unchanged, the bond’s price one year from now will be lower than it is today.

d. The bond should currently be selling at its par value.

e. If market interest rates remain unchanged, the bond’s price one year from now will be higher than it is today.

15. Suppose the real risk-free rate is 3.50% and the future rate of inflation is expected to be constant at 2.20%. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

a. 5.14%

b. 5.42%

c. 5.70%

d. 5.99%

e. 6.28%

16. Suppose 1-year T-bills currently yield 7.00% and the future inflation rate is expected to be constant at 3.20% per year. What is the real risk-free rate of return, r*? Disregard any cross-product terms, i.e., if averaging is required, use the arithmetic average.

a. 3.80%

b. 3.99%

c. 4.19%

d. 4.40%

e. 4.62%

17. Assume that interest rates on 20-year Treasury and corporate bonds are as follows:

T-bond = 7.72% AAA = 8.72% A = 9.64% BBB = 10.18%

The differences in these rates were probably caused primarily by:

a. Tax effects.

b. Default and liquidity risk differences.

c. Maturity risk differences.

d. Inflation differences.

e. Real risk-free rate differences.

18. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.

b. The discount rate increases.

c. The riskiness of the investment’s cash flows decreases.

d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.

e. The discount rate decreases.

19. Assume that inflation is expected to decline steadily in the future, but that the real risk-free rate, r*, will remain constant. Which of the following statements is CORRECT, other things held constant?

a. If the pure expectations theory holds, the Treasury yield curve must be downward sloping.

b. If the pure expectations theory holds, the corporate yield curve must be downward sloping.

c. If there is a positive maturity risk premium, the Treasury yield curve must be upward sloping.

d. If inflation is expected to decline, there can be no maturity risk premium.

e. The expectations theory cannot hold if inflation is decreasing.

20. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.

a. True

b. False