FIN 3880 midterm review
Which of the following is true? A) With any random distribution of asset returns, you can perfectly predict the future realization of the price B) With correctly estimated mean and standard deviation of the return of an asset, we accurately understand the potential risks associated with the investment return if we assume normality on the return of the asset C) Assuming normality helps us predict the changes in asset price up to 10 years into the future D) One of the shortcomings of assuming normality is that the return of the portfolio of assets whose returns are normally distributed is not normally distributed E) Once normality on the stock return is assumed, investors do not have to worry about the future distribution of the return
B) With correctly estimated mean and standard deviation of the return of an asset, we accurately understand the potential risks associated with the investment return if we assume normality on the return of the asset
Which is generally considered to be relatively more safe: Corporate coupon bonds or a derivative security on the public company's stock?. A) Derivative Security B) Common stock C) Corporate coupon bond D) Both are risk-free E) Cannot judge from the information given
C) Corporate coupon bond
In a simple CAPM world which of the following statements is (are) correct? I. All investors will choose to hold the market portfolio, which includes only equity assets in the world. II. Investors' complete portfolio will not vary depending on their risk aversion. III. The return per unit of risk will be identical for all individual assets. IV. The market portfolio will be on the efficient frontier, and it will be the optimal risky portfolio. A) I, II, and III only B) II, III, and IV only C) I, III, and IV only D) I, II, and IIV only E) I, II, III, and IV
C) I, III, and IV only
Which of the following is FALSE? A) CAPM is an equilibrium model that examines what happens with the return of individual security when every investor with the same investment horizon chases alpha in the market B) According to CAPM, the market beta is always 1 C) Multi-factor pricing model is always superior to CAPM and has a very legitimate theoretical background D) CAPM says that the only source of additional return is when the beta of the stock is higher, or taking more market risk exposure E) In a well-diversified portfolio of assets, the only component that will contribute to the portfolio risk is the beat of each stock
C) Multi-factor pricing model is always superior to CAPM and has a very legitimate theoretical background
You are considering adding new security to your portfolio. To decide whether you should add the security, you need to know the security's: I. Expected return II. Standard deviation III. Correlation with your existing portfolio IV. Market risk premium A) IV B) I and II C) II and IV D) I, II, and III E) I, II, and IV
D) I, II, and III
According to Tobin's separation property, portfolio choice can be separated into two independent tasks consisting of ________ and ________. A) Identifying all investor-imposed constraints / identifying the set of securities that conform to the investor's constraints and offer the best risk-return trade-offs B) Identifying the investor's degree of risk aversion / choosing securities from industry groups that are consistent with the investor's risk profile C) Choosing which risky assets an investor prefers according to the investor's risk-aversion level / minimizing the CAL by lending at the risk-free rate D) Identifying the optimal risky portfolio / constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion
D) Identifying the optimal risky portfolio / constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion
Preferred stock is like long-term debt in that ________. A) It gives the holder voting power in the firm's decision-making process B) The preferred dividend is a tax-deductible revenue for the firm C) In the event of bankruptcy preferred stock has superior status with debt D) It promises to pay its holder a fixed stream of income each y
D) It promises to pay its holder a fixed stream of income each y
What is the purpose of the investment? A) To expose your wealth to company-specific risk B) To enjoy the thrill of betting on the outcome of March Madness C) To minimize return while maximizing the risk D) To identify risk-minimizing opportunities and use NPV to make decision E) To smooth out the level of consumption across different time periods by identifying opportunities with a positive risk premium
E) To smooth out the level of consumption across different time periods by identifying opportunities with a positive risk premium
Derek is trying to evaluate a performance of the mutual fund he is currently invested in. Given the below makeup of the portfolio and that the current equity market return is 9% and the risk-free rate of return is 3.5%, should he continue to invest in this fund? Why or why not? Stock Investment Expected Return Beta Apple $300,000 35% 1.81Pear $100,000 15% 0.5 Googol $250,000 25% 1.32Gargle $150,000 17% 0.9 Macrosoft $200,000 31% 1.66
Portfolio beta:0.3*1.81 + 0.1*0.5 + 0.25*1.32 + 0.15*0.9 + 0.2*1.66 = 1.39 Portfolio's expected return predicted by CAPM:0.035 + 1.39*(0.09-0.035) = 11.15% Portfolio's actual expected return:0.3*0.35 + 0.1*0.15 + 0.25*0.25 + 0.15*.17 + 0.2*.31 = 27% Because the actual return is expected to be greater than what CAPM predicts, you should continue to invest.
Two assets have the following expected returns and standard deviations when the risk-free rate is 3.5%:Asset A's E(return) = 20% / σ(A) = 20%Asset B's E(return) = 25% / σ(B) = 27%An investor with a risk aversion of A = 3 would find that the asset ________ preferrable on a risk-return basis
Price of Risk for A = (0.2-0.035)/(0.2^2) = 4.125 Price of Risk for B = (0.25-0.035)/(0.27^2) = 2.95 Because the asset A has a higher price of risk than 3, the asset A is the one this investor is willing to buy despite the risk because it exceeds the required price of risk.
An investor forecasts the likelihood of different economic situations in the future. She expects the current economic situation will continue at 50% chance, the economic boom to emerge at 30%, and the recession to arrive at 20% chances. With each economic situation, she expects her portfolio to generate 10%, 25%, and -10% returns, respectively. Her portfolio's expected rate of return and the standard deviation are ___________ and________, respectively.
Return: 0.5*0.1 + 0.3*0.25 + 0.2*(-0.1) = 10.5%Standard Deviation: √𝟎. 𝟓(𝟎. 𝟏 − 𝟎. 𝟏𝟎𝟓)𝟐 + 𝟎. 𝟑(𝟎. 𝟐𝟓 − 𝟎. 𝟏𝟎𝟓)𝟐 + 𝟎. 𝟐(−𝟎. 𝟏 − 𝟎. 𝟏𝟎𝟓)𝟐 = 𝟏𝟐. 𝟏𝟑%
You are considering investing $10,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 2% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 50% and 50%, respectively. X has an expected rate of return of 20%, and Y has an expected rate of return of 30%. The dollar values of your positions in X, Y, and Treasury bills would be ________, ________, and ________, respectively, if you decide to hold a complete portfolio that has an expected return of 10%.
Risky Asset's return = 0.5*0.2 + 0.5*0.3 = 0.25 Weight of the risky asset for the complete portfolio: 0.1=0.25*y + (1-y)*0.02 The percentage weight to risky portfolio y=0.347826 Risk free asset allocation = 1-0.347826 = 0.652174 Therefore, the respective dollar amount that should be invested to the risky asset and the risk-free asset are $3478.26 and $6521.74. Because the optimal weight is 50%/50%, the dollar amounts invested to asset X and Y are $1739.13 for both. $1739.13, $1739.13, $6521.74
Consider a Treasury bill with a rate of return of 2.5% and the following risky securities:Security A: E(r) = 10%; variance = 0.01Security B: E(r) = 20%; variance = 0.03Security C: E(r) = 30%; variance = 0.07Security D: E(r) = 40%; variance = 0.14The investor must develop a complete portfolio by combining the risk-free asset with oneof the securities mentioned above. The security the investor should choose as part of her complete portfolio to achieve the best CAL would be Security ________
Slope of CAL = Sharpe Ratio Sharpe Ratio of A: 0.75 B:1.01 C:1.04 D:1.00 C has the best Sharpe Ratio
Consider a Treasury bill with a rate of return of 3.5% and the following risky securities: Security A: E(r) = 10%; variance = 0.011Security B: E(r) = 20%; variance = 0.033Security C: E(r) = 30%; variance = 0.077Security D: E(r) = 40%; variance = 0.1414The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor should choose as part of her complete portfolio to achieve the best CAL would be Security ________.
Slope of CAL = Sharpe Ratio Sharpe Ratio of A: (0.1-.035)/√(0.011) = 0.619 B: 0.908 C: 0.955 D: 0.971 D has the best Sharpe Ratio
You invest $100,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 14% and a standard deviation of 25% and a Treasury bill with a rate of return of 5%. How much money should be invested in the risky asset to form a portfolio with a target standard deviation of 18%?
Target standard deviation = y*standard deviation of a risky asset. 18=y*.25 → y=.18/.25 = 0.72 0.72*100,000 = 72,000
Adding additional risky assets to the investment opportunity set will generally move theefficient frontier ________ and to the ________. A) Up / Left B) Up / Right C) Down / Left D) Down / Righ
A) Up / Left
If enough investors decide to sell stocks, they are likely to drive down stock prices, thereby causing ________ and ________. A) expected returns to rise; risk premiums to rise B) expected returns to rise; risk premiums to fall C) expected returns to fall; risk premiums to rise D) expected returns to fall; risk premiums to fall
A) expected returns to rise; risk premiums to rise
Two investment advisers are comparing performance. Adviser A averaged a 18% return with a portfolio beta of 1.3, and adviser B averaged a 15% return with a portfolio beta of0.9. If the T-bill rate was 3% and the market return during the period was 13%, which adviser was the better stock picker and why?
B, because of the high alpha A:earned return: 18%expected return from CAPM: 0.03 + 1.3*(.13-.03) = .16A's Alpha = .18-.16 = 0.02 B:earned return: 15%expected return from CAPM: 0.03 + 0.9*(.13-.03) = .12B's Alpha = .15-.12 = 0.03
If enough investors decide to purchase stocks, they are likely to drive up stock prices, thereby causing ________ and ________. A) expected returns to rise; risk premiums to fall B) expected returns to fall; risk premiums to rise C) expected returns to fall; risk premiums to fall D) expected returns to rise; risk premiums to rise
C) expected returns to fall; risk premiums to fall
In his famous critique of the CAPM, Roll argued that the CAPM ________. A) should be replaced by the APT B) is a limited model because systematic risk can never be eliminated entirely C) always gets rid of the risk, so it is the most efficient way to manage risk D) should be replaced by the Fama-French three-factor model E) is not testable because the true market portfolio theorized in CAPM can never be observed
E) is not testable because the true market portfolio theorized in CAPM can never be observed
Recall information from Question 15: Now, suppose you are considering to add stock C to the currently established optimal risky portfolio that used A and B, of which you already calculated each weight in Question 15. If the stock C has 10% return with 10% standard deviation and has -1 correlation coefficient with the already established optimal risky portfolio, what is the expected return of the newly calculated optimal risky portfolio that also includes stock C?(Hint: treat the optimal risky portfolio formed from Q15 as a single asset that has a distinct return and risk calculated from Q15 and Q16, and form a new optimal risky portfolio with C)
You want to use the answers from Q15 and Q16 as the input to the new calculation. Therefore,𝒘𝟏= [𝟎. 𝟏𝟕𝟖𝟏 − 𝟎. 𝟎𝟑](𝟎.𝟏𝟐) − [𝟎.𝟏 − 𝟎.𝟎𝟑]𝟎. 𝟏𝟒𝟎𝟖 × 𝟎.𝟏 × (−𝟏)[𝟎.𝟏𝟕𝟖𝟏 − 𝟎.𝟎𝟑](𝟎.𝟏𝟐) + [𝟎.𝟏 − 𝟎.𝟎𝟑](𝟎.𝟏𝟒𝟎𝟖𝟐) − [𝟎.𝟏𝟔 − 𝟎.𝟎𝟑 + 𝟎.𝟐 − 𝟎.𝟎𝟑]𝟎.𝟏𝟒𝟎𝟖 × 𝟎.𝟏 × (−𝟏) =0.4153 W2 = 0.5847 0.4153*0.1781 + 0.5847*0.1 = 13.24%
The geometric average of 10%, 20%, and -15% is ________.
√(𝟏 + 𝟎. 𝟏) × (𝟏 + 𝟎. 𝟐) × (𝟏 + (−𝟎. 𝟏𝟓))𝟑 − 𝟏3.91%
An investor can design a risky portfolio based on two stocks, A and B. Stock A has anexpected return of 15% and a standard deviation of return of 20%. Stock B has an expectedreturn of 25% and a standard deviation of return of 30%. The correlation coefficientbetween the returns of A and B is -0.01. The risk-free rate of return is 3%. The expectedreturn on the optimal risky portfolio is approximately _______.(Hint: Find weights first by using the weights of the optimal risky portfolio equa
𝒘𝟏= [𝟎. 𝟏𝟓 − 𝟎. 𝟎𝟑](𝟎. 𝟑𝟐) − [. 𝟐𝟓 − 𝟎. 𝟎𝟑]𝟎. 𝟐 × 𝟎. 𝟑 × (−𝟎. 𝟎𝟏)/[𝟎. 𝟏𝟓 − 𝟎. 𝟎𝟑](𝟎. 𝟑𝟐) + [𝟎. 𝟐𝟓 − 𝟎. 𝟎𝟑](𝟎. 𝟐𝟐) − [𝟎. 𝟏𝟓 − 𝟎. 𝟎𝟑 + 𝟎. 𝟐𝟓 − 𝟎. 𝟎𝟑]𝟎. 𝟐 × 𝟎. 𝟑 × (−𝟎. 𝟎𝟏)=0.55201 W2 = 0.44799 0.55201*0.15 + 0.44799*0.25 = 19.48%
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 16% and a standard deviation of return of 20%. Stock B has an expected return of 20% and a standard deviation of a return of 25%. The correlation coefficient between the returns of A and B is -0.2. The risk-free rate of return is 3%. The expected return on the optimal risky portfolio is approximately _______.(Hint: Find weights first by using the weights of the optimal risky portfolio equation)
𝒘𝟏= [𝟎.𝟏𝟔 − 𝟎.𝟎𝟑](𝟎.𝟐𝟓𝟐) − [.𝟐𝟎 − 𝟎.𝟎𝟑]𝟎.𝟐 × 𝟎.𝟐𝟓 × (−𝟎.𝟐)[𝟎.𝟏𝟔 − 𝟎.𝟎𝟑](𝟎.𝟐𝟓𝟐) + [𝟎.𝟐 − 𝟎.𝟎𝟑](𝟎.𝟐𝟐) − [𝟎.𝟏𝟔 − 𝟎.𝟎𝟑 + 𝟎.𝟐 − 𝟎.𝟎𝟑]𝟎.𝟐 × 𝟎.𝟐𝟓 × (−𝟎.𝟐) =0.5481 W2 = 0.4519 0.5481*0.16 + 0.4519*0.2 = 17.81%
The two-factor model on a stock provides a risk premium for exposure to market risk of8%, a risk premium for exposure to interest rate risk of (-2.5%), and a risk-free rate of 3%.The beta for exposure to market risk is 1.5, and the beta for exposure to interest rate riskis 2. What is the expected return on the stock
0.03 + 1.5*.08 + 2*(-0.025) = 10%
Your investment has a 25% chance of earning a 25% rate of return, a 60% chance ofearning a 10% rate of return, and a 15% chance of losing 15%. What is your expectedreturn on this investment
0.25*0.25+0.6*0.1+0.15*(-0.15) = 10%
An investor invests 60% of her wealth in a risky asset with an expected rate of return of20% and a standard deviation of 35%, and she puts 40% in a Treasury bill that pays 5%.Her portfolio's expected rate of return and standard deviation are ___________ and________ respectively.
0.6*0.2 + 0.4*0.05 = 0.14 0.6*0.35 = .21 14% / 21%
Assign ranks to below securities by the increasing level of general riskiness as an investment medium, where "1" represents the most safe, and "7" the most risky. You can write the number rank next to each security Security Description A publicly traded common share of Microsoft Inc. A equity index that concentrates on the semi-conductor industry 10-year maturity corporate bond with AAA rating OTC call option on Autotrader Inc. issued by JP Morgan Chase Stable cryptocurrency whose value may be pegged to USD A private share of preferred equity issue by Publix Co. A privately issued mortgage backed bond with CCC credit rating
A publicly traded common share of Microsoft Inc. 5 A equity index that concentrates on the semi-conductor industry 4 10-year maturity corporate bond with AAA rating 1 OTC call option on Autotrader Inc. issued by JP Morgan Chase 6 Stable cryptocurrency whose value may be pegged to USD 7 A private share of preferred equity issue by Publix Co. 3 A privately issued mortgage backed bond with CCC credit rating 2
Two investment advisers are comparing performance. Adviser A averaged a 13.5% return with a portfolio beta of 1.4, and adviser B averaged a 10% return with a portfolio beta of0.8. If the T-bill rate was 3.5% and the market return during the period was 8.5%, which adviser was the better stock picker and why?
A's expected return from CAPM: 0.035 + 1.4*(0.085-0.035) = 10.5% B's expected return from CAPM: 0.035 + 0.8*(0.085-0.035) = 7.5% A's alpha = 13.5% - 10.5% = 3% B's alpha = 10% - 7.5% = 2.5% A is a better adviser because of the higher alpha generated.
According to Separation Property, portfolio choice can be separated into two independent tasks consisting of ________ and ________. A) Identifying the optimal risky portfolio / constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion B) Identifying all investor-imposed constraints / identifying the set of securities that conform to the investor's constraints and offer the best risk-return trade-offs C) Identifying the investor's degree of risk aversion / choosing securities from industry groups that are consistent with the investor's risk profile D) Choosing which risky assets an investor prefers according to the investor's risk-aversion level / minimizing the CAL by lending at the risk-free rate E) Creating a risky portfolio by achieving the target risk / understanding investment horizon required for the target return
A) Identifying the optimal risky portfolio / constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion
Adding additional risky assets to the investment opportunity set will generally move the efficient frontier ________ and to the ________. A) Up / Left B) Up / Right C) Down / Left D) Down / Right E) Does not move regardless of the risk level
A) Up / Left
Consider an investment opportunity set formed with two securities that are perfectlynegatively correlated. The global minimum-variance portfolio has a standard deviationthat is always ________. A) -1 B) 0 C) 1 D) Cannot determine from the given information
B) 0
In a simple CAPM world which of the following statements is (are) correct? I. No investors will choose to hold the market portfolio, which includes only equity assets in the world. II. Investors' complete portfolio will vary depending on their risk aversion. III. The return per unit of risk will be identical for all individual assets. IV. The market portfolio will be on the efficient frontier, and it will be the optimal risk portfolio. A) I, II, and III only B) II, III, and IV only C) I, III, and IV only D) I, II, III, and IV
B) II, III, and IV only
What is the purpose of the investment? A) To expose your wealth to unnecessary speculative risk B) To smooth out the level of consumption across different time periods C) To enjoy the thrill of betting on assets that you like the sound of their names D) To minimize return while maximizing the r
B) To smooth out the level of consumption across different time periods
What is the Bond Equivalent Yield of a treasury bill that is currently priced at $9957 with 181 days to maturity?
Using the bond equivalent yield formula, 𝟏𝟎𝟎𝟎𝟎−𝟗𝟗𝟓𝟕/𝟗𝟗𝟓𝟕 × 𝟑𝟔𝟓/𝟏𝟖𝟏 = 𝟎.𝟖𝟕𝟏%
You invest $100,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 10% and a standard deviation of 20% and a Treasury bill with a rate of return of 2%. How much money should be invested in the risky asset to form a portfolio with an expected return of 6%?
Using the formula for return of a complete portfolio, 0.06= y*0.1 + (1-y)0.02y=0.5 Therefore, 0.5*100000 = $50,000
Using the risk and return profile calculated in Q12 and Q13, what is the percentage weightthat you need to invest in the optimal risky portfolio if you want your complete portfolioto achieve a 10% return?
Using the formula for the complete portfolio, 0.1 = y*(.1948) + (1-y)*0.03Y=42.48%
A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 20%, while stock B has a standard deviation of return of 30%. The correlation coefficient between the returns on A and B is -0.2. Stock A comprises 40% of the portfolio, while stock B comprises 60% of the portfolio. The standard deviation of the return on this portfolio is ________.
Using the formula for the standard deviation of two-asset risky portfolio, √(𝟎. 𝟒𝟐 × 𝟎. 𝟐𝟐) + (𝟎. 𝟔𝟐 × 𝟎. 𝟑𝟐) + 𝟐 × 𝟎. 𝟔 × 𝟎. 𝟒 × 𝟎. 𝟐 × 𝟎. 𝟑 × (−𝟎. 𝟐) =18.18%
Using the calculated optimal weights and information from Question 15, what is the standard deviation of returns on the optimal risky portfolio ________?
Using the standard deviation of risky portfolio formula,𝝈 = √𝟎.𝟓𝟒𝟖𝟏𝟐 × 𝟎.𝟐𝟐 + 𝟎.𝟒𝟓𝟏𝟗𝟐 × 𝟎.𝟐𝟓𝟐 + 𝟐 × 𝟎.𝟓𝟒𝟖𝟏 × 𝟎.𝟒𝟓𝟏𝟗 × 𝟎.𝟐 × 𝟎.𝟐𝟓 × −𝟎.𝟐 = 𝟏𝟒.𝟎𝟖%
A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 30%, while stock B has a standard deviation of return of 18%. The correlation coefficient between the returns on A and B is 0.01. Stock A comprises 65% of the portfolio, while stock B comprises 35% of the portfolio. The standard deviation of the return on this portfolio is ________
Using the standard deviation of risky portfolio formula,𝝈 = √𝟎.𝟔𝟓𝟐 × 𝟎.𝟑𝟐 + 𝟎.𝟑𝟓𝟐 × 𝟎.𝟏𝟖𝟐 + 𝟐 × 𝟎.𝟔𝟓 × 𝟎.𝟑𝟓 × 𝟎.𝟑 × 𝟎.𝟏𝟖 × 𝟎.𝟎𝟏= 𝟐𝟎.𝟓𝟓%
You are considering investing $100,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 3% and a risky portfolio, P, constructed with assets A and B from Question 15. Using the information and derived weights from Question 15,what is the dollar values of your investment positions in A, B, and Treasury bills, respectively, if you decide to hold a complete portfolio that has an expected return of 12%?
Using the target return formula,0.12 = 0.1781*y + (1-y)*0.03 Y=0.6078 Therefore, the amount of money invested to the risky portfolio should be $60,780 and $39,220 for the risk-free asset. Because the question asks the dollar allocation between A and B, For A: $60,780*0.5481 = $33,314 For B: $60,780*0.4519 = $27,466
Using the calculated optimal weights and information from Question 12, what is the standard deviation of returns on the optimal risky portfolio ________
Using the weights calculated from Q.12, √(𝟎. 𝟓𝟓𝟐𝟎𝟏𝟐 × 𝟎. 𝟏𝟓𝟐) + (𝟎. 𝟒𝟒𝟕𝟗𝟗𝟐 × 𝟎. 𝟐𝟓𝟐) + 𝟐 × 𝟎. 𝟓𝟓𝟐𝟎𝟏 × 𝟎. 𝟒𝟒𝟕𝟗𝟗 × 𝟎. 𝟏𝟓 × 𝟎. 𝟐𝟓 × (−𝟎. 𝟎𝟏) =17.31%
