Mini Case on Risk Return 1-Solution

Mini Case on Risk & ReturnYou working for a large financial services corporation have the following investment alternatives.

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

Estimated Returns on Alternate Investments State of T-Bills Alta

Economy0.1 8% -22% 28% 10% -13% 3%

0.2 8% -2% 14.70% -10% 1% ?

Average 0.4 8% 20% 0 7% 15% 10%0.2 8% 35% -10% 45% 29%

Boom 0.1 8% 50% -20% 30% 43% ?? ? 1.74% ? 15% ?

? ? 13.36 ? 15.3 ?

CV ? ? 7.68 ? ? ?Beta ? ? -0.86 ? ? ?

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

Now answer the following questions:

Ans.

Year Market PQ

1 25.70% 40%

Probability

Repo Men

American Foam*

Market Portfolio

2 Stock Portfolio (Alta/Repo)

Recession

Below average

Above average

Expected return

Standard deviation

a)      What are investment returns? What is the return on an investment that costs Rs 1000, fetches dividend of Rs 20 and is sold after one year for Rs 1100?

b)      (1)Why is Treasury bills return independent of the state of economy? Do they promise a completely risk free return? (2) Why are Alta’s returns expected to move with the economy whereas Repo Men’s expected to move counter to the economy? c)      Fill up all the blanks in the above table and show the working.d)     You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.e)      Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as a better measure of stand alone risk than standard deviation when the alternatives being considered have widely differing expected returns. Calculate missing CVs. Does the CV produce the same risk rankings as the standard deviation? f)       Suppose you created a 2 stock portfolio by investing Rs 50000 in Alta and Rs 50000 in Repo Men. (1)Calculate the expected return, standard deviation and CV for this portfolio and fill up the Table. (2) How does the risk of this portfolio compare with the individual stocks held in isolation ?g)      Suppose an investor starts with a portfolio consisting of one randomly selected stock listed on BSE. What would happen to the risk and the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of portfolio with, say, 2 stocks and with, say, 5 stocks so selected.h)      (1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?i)        How is market risk measured for individual securities? How are beta coefficients calculated?j)        Suppose you have following historical returns for the stock market and for another Company called PQ. Calculate Beta for PQ and interpret results.

2 8% -15%3 -11% -15%4 15% 35%5 32.50% 10%6 13.70% 30%7 40% 42%8 10% -10%9 -10.80% -25%

10 -13.10% 25%

Security Return %

Alta 17.4 1.29Market 15 1

13.8 0.68

T-Bills 8 01.7 -0.86

l.(1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative and then graph the relationship between the expected and required rates of return.(2)How do the expected rates of return compare with the required rates of return? (3) Does the fact that Repo Men has an expected rate of return less than T-bill rate make any sense?(4)What would be the market risk and the required rate of return of a 50-50 portfolio of Alta and Repo Men? Of Alta and American Foam?

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

k)      The expected rates of return and the beta coefficients of the following alternatives as supplied by the Company’s computer programme are as follows :Risk(Beta)

American Foam

Repo Men

(1)   Do expected returns appear to be related to each alternative’s market risk?(2)   Is it possible to choose among alternatives on the basis of the information developed so far?

You working for a large financial services corporation have the following investment alternatives.

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

What are investment returns? What is the return on an investment that costs Rs 1000, fetches dividend of Rs 20 and is sold after one year for Rs 1100?

(1)Why is Treasury bills return independent of the state of economy? Do they promise a completely risk free return? (2) Why are Alta’s returns expected to move with the economy whereas Repo Men’s expected to move counter to the economy?

You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as a better measure of stand alone risk than standard deviation when the alternatives being considered have widely differing expected returns. Calculate missing CVs. Does the CV produce the same risk rankings as the standard deviation? Suppose you created a 2 stock portfolio by investing Rs 50000 in Alta and Rs 50000 in Repo Men. (1)Calculate the expected return, standard deviation and CV for this portfolio and fill up the Table. (2) How does the risk of this portfolio compare with the individual stocks held in isolation ?Suppose an investor starts with a portfolio consisting of one randomly selected stock listed on BSE. What would happen to the risk and the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of portfolio with, say, 2 stocks and with, say, 5 stocks so selected.(1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?How is market risk measured for individual securities? How are beta coefficients calculated?Suppose you have following historical returns for the stock market and for another Company called PQ. Calculate Beta for PQ and interpret results.

l.(1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative and then graph the relationship between the expected and required rates of return.

(3) Does the fact that Repo Men has an expected rate of return less than T-bill rate make any sense?(4)What would be the market risk and the required rate of return of a 50-50 portfolio of Alta and Repo Men? Of Alta and American Foam?

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

The expected rates of return and the beta coefficients of the following alternatives as supplied by the Company’s computer programme are as follows :

Is it possible to choose among alternatives on the basis of the information developed so far?

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

(1)Why is Treasury bills return independent of the state of economy? Do they promise a completely risk free return? (2) Why are Alta’s returns expected to move with the economy whereas Repo Men’s expected to move counter to the economy?

You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as a better measure of stand alone risk than standard deviation when the alternatives being considered have widely differing expected returns. Calculate missing CVs. Does the CV produce the same risk rankings as the standard deviation? Suppose you created a 2 stock portfolio by investing Rs 50000 in Alta and Rs 50000 in Repo Men. (1)Calculate the expected return, standard deviation and CV for this portfolio and fill up the Table. (2) How does the risk of this portfolio compare with the individual stocks held in isolation ?Suppose an investor starts with a portfolio consisting of one randomly selected stock listed on BSE. What would happen to the risk and the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of portfolio with, say, 2 stocks and with, say, 5 stocks so selected.(1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?

l.(1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative and then graph the relationship between the expected and required rates of return.

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as a better measure of stand alone risk than standard deviation when the alternatives being considered have widely differing expected returns. Calculate missing CVs. Does the CV produce the same risk rankings as the standard deviation? Suppose you created a 2 stock portfolio by investing Rs 50000 in Alta and Rs 50000 in Repo Men. (1)Calculate the expected return, standard deviation and CV for this portfolio and fill up the Table. (2) How does the risk of this portfolio compare with the individual stocks held in isolation ?Suppose an investor starts with a portfolio consisting of one randomly selected stock listed on BSE. What would happen to the risk and the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of portfolio with, say, 2 stocks and with, say, 5 stocks so selected.(1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

Mini Case on Risk & Return

You working for a large financial services corporation have the following investment alternatives.

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

Estimated Returns on Alternate Investments State of Probability T-Bills AltaEconomyRecession 0.1 8% -22% 28% 10% -13% 3%Below average 0.2 8% -2% 14.70% -10% 1% 6.4%

Average 0.4 8% 20% 0 7% 15% 10%0.2 8% 35% -10% 45% 29% 12.5%

Boom 0.1 8% 50% -20% 30% 43% 15.0%8.00% 17.40% 1.74% 13.80% 15.00% 9.57%

0.0% 20.0%13.36%

18.82% 15.34% 3.34%

CV 0.00 1.15 7.68 1.36 1.02 0.35 Beta 0 1.29 -0.86 0.68 1 ?

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

Now answer the following questions:a) What are investment returns? What is the return on an investment that costs Rs 1000, fetches dividend of Rs 20 and is sold after one year for Rs 1100?Ans. The profit or return which we get on an investment is termed as investment return. It can be calculated as :

Investment rate of return = Annual income + Ending price -Beginning price Beginning price

b) (1)Why is Treasury bills return independent of the state of economy? Do they promise a completely risk free return? (2) Why are Alta’s returns expected to move with the economy whereas Repo Men’s expected to move counter to the economy? Ans. The return on Treasury bills is constant at all levels of the State of economy. They are short term govt. Bonds which have a fixed rate of return and hence it does not fluctuate with the change in the market. They posses a very low level of risk or no risk which is visible in the above table. The Standard Deviation and the coeficient of variable is 0.

From the above table we can conclude that the beta for Alta is 1.29 which shows that it moves with the economy and the beta of Repo Men is -0.86 which indicates that it moves counter to the economy. Hence, Alta's returns are expected to move with the economy whereas Repo Men's expected to move counter to the economy.

c) Fill up all the blanks in the above table and show the working.Ans. Please refer the above table.

d) You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.Ans. With the help of Standard deviation we are able to find Beta which shows the risk factor in a particular stock.

e) Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as a better measure of stand alone risk than standard deviation when the alternatives being considered have widely differing expected returns. Calculate missing CVs. Does the CV produce the same risk rankings as the standard deviation? Ans. No, the CV does not produce the same risk rankings as the standard deviation.

Repo Men

American Foam*

Market Portfolio

2 Stock Portfolio (Alta/Repo)

Above average

Expected return

Standard deviation

f) Suppose you created a 2 stock portfolio by investing Rs 50000 in Alta and Rs 50000 in Repo Men. (1)Calculate the expected return, standard deviation and CV for this portfolio and fill up the Table. (2) How does the risk of this portfolio compare with the individual stocks held in isolation ?g) Suppose an investor starts with a portfolio consisting of one randomly selected stock listed on BSE. What would happen to the risk and the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of portfolio with, say, 2 stocks and with, say, 5 stocks so selected.Ans. If an investor invests on only one stock then the risk factor is higher compared to the investment done in more than one stock. If an investor invests in many stocks then he can reduce the unique risk which even can be null depending on the number of investments made in different sectors.

h) (1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?Ans. Yes, portfolio effects impact the way investors think about the risk of individual stocks.

Yes, we can expect to earn a risk premium as the risk taken by us is higher. The higher the risk, the higher risk premium can be expected.

i) How is market risk measured for individual securities? How are beta coefficients calculated?Ans. Market risk for individual securities is measured through beta. The average for Beta is always 1. The formula to calculate beta is as follows.

Beta = Sum of Co-variance of individual stock (Standard deviation of Market)^2

j) Suppose you have following historical returns for the stock market and for another Company called PQ. Calculate Beta for PQ and interpret results.

Year Market PQ1 25.70% 40% 14.7 28.3 216.09 416.012 8% -15% -3 -26.7 9 80.13 -11% -15% -22 -26.7 484 587.44 15% 35% 4 23.3 16 93.25 32.50% 10% 21.5 -1.7 462.25 -36.556 13.70% 30% 2.7 18.3 7.29 49.417 40% 42% 29 30.3 841 878.78 10% -10% -1 -21.7 1 21.79 -10.80% -25% -21.8 -36.7 475.44 800.06

10 -13.10% 25% -24.1 13.3 580.81 -320.53Total 110.00% 117% 3092.88 2569.5

Ans. Beta = Sum of Co-variance of individual stock = 2569.5 (Standard deviation of Market)^2 3092.88

The beta is just below the average which is fine with this stock. The returns are just below the average but there is not much difference.

k) The expected rates of return and the beta coefficients of the following alternatives as supplied by the Company’s computer programme are as follows :Security Return % Risk(Beta)Alta 17.4 1.29Market 15 1American Foam 13.8 0.68T-Bills 8 0Repo Men 1.7 -0.86

-1 Do expected returns appear to be related to each alternative’s market risk?Ans. Yes, the expected returns are related to each alternative's market risk. As the risk is higher, the return is also higher.

-2 Is it possible to choose among alternatives on the basis of the information developed so far?

Market variance

PQ variance

Sq of Mkt var

Co-variance

Ans. Yes, it is possible to choose. Alta has the maximum return which is favourably good in terms of returns. But, also the risk factor is higher.

l.(1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative and then graph the relationship between the expected and required rates of return.(2)How do the expected rates of return compare with the required rates of return? (3) Does the fact that Repo Men has an expected rate of return less than T-bill rate make any sense?(4)What would be the market risk and the required rate of return of a 50-50 portfolio of Alta and Repo Men? Of Alta and American Foam?

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

Mini Case on Risk & Return

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

What are investment returns? What is the return on an investment that costs Rs 1000, fetches dividend of Rs 20 and is sold after one year for Rs 1100?The profit or return which we get on an investment is termed as investment return. It can be calculated as :

Annual income + Ending price -Beginning price = 20+1100-1000 = 12.00%Beginning price 1000

(1)Why is Treasury bills return independent of the state of economy? Do they promise a completely risk free return? (2) Why are Alta’s returns expected to move with the economy whereas Repo Men’s expected to move counter to the economy? The return on Treasury bills is constant at all levels of the State of economy. They are short term govt. Bonds which have a fixed rate of return and hence it does not fluctuate with the change in the market. They posses a very low level of risk or no risk which is visible in the above table. The Standard Deviation and the coeficient of variable is 0. From the above table we can conclude that the beta for Alta is 1.29 which shows that it moves with the economy and the beta of Repo Men is -0.86 which indicates that it moves counter to the economy. Hence, Alta's returns are expected to move with the economy whereas Repo Men's expected to move counter to the economy.

You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.With the help of Standard deviation we are able to find Beta which shows the risk factor in a particular stock.

Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as a better measure of stand alone risk than standard deviation when the alternatives being considered have widely differing expected returns. Calculate missing CVs. Does the CV produce the same risk rankings as the standard deviation? No, the CV does not produce the same risk rankings as the standard deviation.

Suppose you created a 2 stock portfolio by investing Rs 50000 in Alta and Rs 50000 in Repo Men. (1)Calculate the expected return, standard deviation and CV for this portfolio and fill up the Table. (2) How does the risk of this portfolio compare with the individual stocks held in isolation ?Suppose an investor starts with a portfolio consisting of one randomly selected stock listed on BSE. What would happen to the risk and the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of portfolio with, say, 2 stocks and with, say, 5 stocks so selected.

If an investor invests on only one stock then the risk factor is higher compared to the investment done in more than one stock. If an investor invests in many stocks then he can reduce the unique risk which even can be null depending on the number of investments made in different sectors.

(1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?Yes, portfolio effects impact the way investors think about the risk of individual stocks. Yes, we can expect to earn a risk premium as the risk taken by us is higher. The higher the risk, the higher risk premium can be expected.

How is market risk measured for individual securities? How are beta coefficients calculated?Market risk for individual securities is measured through beta. The average for Beta is always 1. The formula to calculate beta is as follows.

Suppose you have following historical returns for the stock market and for another Company called PQ. Calculate Beta for PQ and interpret results.

= 0.830779

The beta is just below the average which is fine with this stock. The returns are just below the average but there is not much difference.

The expected rates of return and the beta coefficients of the following alternatives as supplied by the Company’s computer programme are as follows :

Yes, the expected returns are related to each alternative's market risk. As the risk is higher, the return is also higher.

Is it possible to choose among alternatives on the basis of the information developed so far?

Yes, it is possible to choose. Alta has the maximum return which is favourably good in terms of returns. But, also the risk factor is higher.

l.(1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative and then graph the relationship between the expected and required rates of return.

(3) Does the fact that Repo Men has an expected rate of return less than T-bill rate make any sense?(4)What would be the market risk and the required rate of return of a 50-50 portfolio of Alta and Repo Men? Of Alta and American Foam?

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

(1)Why is Treasury bills return independent of the state of economy? Do they promise a completely risk free return? (2) Why are Alta’s returns expected to move with the economy whereas Repo Men’s expected to move counter to the economy? The return on Treasury bills is constant at all levels of the State of economy. They are short term govt. Bonds which have a fixed rate of return and hence it does not fluctuate with the change in the market. They posses a very low level of risk or no risk which is visible in the above table. The Standard Deviation and the coeficient of variable is 0. From the above table we can conclude that the beta for Alta is 1.29 which shows that it moves with the economy and the beta of Repo Men is -0.86 which indicates that it moves counter to the economy. Hence, Alta's returns are expected to move with the economy whereas Repo Men's expected to move counter to the economy.

You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.

Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as a better measure of stand alone risk than standard deviation when the alternatives being considered have widely differing expected returns. Calculate missing CVs. Does the CV produce the same risk rankings as the standard deviation?

Suppose you created a 2 stock portfolio by investing Rs 50000 in Alta and Rs 50000 in Repo Men. (1)Calculate the expected return, standard deviation and CV for this portfolio and fill up the Table. (2) How does the risk of this portfolio compare with the individual stocks held in isolation ?Suppose an investor starts with a portfolio consisting of one randomly selected stock listed on BSE. What would happen to the risk and the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of portfolio with, say, 2 stocks and with, say, 5 stocks so selected.

If an investor invests on only one stock then the risk factor is higher compared to the investment done in more than one stock. If an investor invests in many stocks then he can reduce the unique risk which even can be null depending on the number of investments made in different sectors.

(1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

The return on Treasury bills is constant at all levels of the State of economy. They are short term govt. Bonds which have a fixed rate of return and hence it does not fluctuate with the change in the market. They posses a very low level of risk or no risk which is visible in the above table. The Standard Deviation and the coeficient of variable is 0. From the above table we can conclude that the beta for Alta is 1.29 which shows that it moves with the economy and the beta of Repo Men is -0.86 which indicates that it moves counter to the economy. Hence, Alta's returns are expected to move with the economy whereas Repo Men's expected to move counter to the economy.

You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.

Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as a better measure of stand alone risk than standard deviation when the alternatives being considered have widely differing expected returns. Calculate missing CVs. Does the CV produce the same risk rankings as the standard deviation?

Suppose an investor starts with a portfolio consisting of one randomly selected stock listed on BSE. What would happen to the risk and the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of portfolio with, say, 2 stocks and with, say, 5 stocks so selected.If an investor invests on only one stock then the risk factor is higher compared to the investment done in more than one stock. If an investor invests in many stocks then he can reduce the unique risk which even can be null depending on the number of investments made in different sectors.

(1) Should portfolio effects impact the way investors think about the risk of individual stocks? (2) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.

You should recognize that basing a decision solely on expected returns is appropriate only for risk neutral individuals. Because your client, like virtually every one, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of the returns. What type of risk is measured by standard deviation? Draw a graph that shows roughly the shape of probability distribution for Alta, American Foam & T-bills.

m.(1)Suppose investors raised their inflation expectations by 3% over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high and low risk securities? (2)Suppose instead their investors’ risk aversion increased enough to cause the market risk premium to increase by 3% (Inflation remains constant). What effect would this have on the SML and on the returns of high and low risk securities?

Your company’s economic forecasting staffs have developed probability estimates for the state of the economy and the security analysts have developed a sophisticated computer programme used for estimating rate of return under each alternate state of economy. Alta is an electronics firm, Repo Men collects past due debts and Amercian Foam manufactures mattresses & foam products. The company also maintains an “index fund” which owns a market weighted fraction of all publicly traded stocks & you can invest in that fund and thus obtain average stock market returns.

*Note that estimated returns of American Foam do not always move in the same direction as the overall economy. Eg. When the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattresses may purchase, instead, a cheaper foam mattress. Under the circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average.