Fin 3050 Exam 3

A portfolio has a Jensen's alpha of .93%, a beta of 1.45, and a CAPM expected return of 8.8%. The risk-free rate is 2.5%. What is the actual return of the portfolio? 7.83% 6.17% 9.73% 21.9% 5.53%.

.0093 = RP − .088; RP = .0973, or 9.73%

A portfolio has a Treynor ratio of .055, a standard deviation of 13.3%, a beta of 1.22, and an expected return of 15.3%. What is the risk-free rate? 7.39% 8.59% 6.18% 7.21% 8.18%

.055 = (.153 − rf) / 1.22; rf = .0859, or 8.59%

A portfolio consists of the following two funds: Fund A Fund B Weight 45% 55% Exp Return 16% 9% Std Dev 21% 11% Corr(A,B) 0.21 Riskfree rate 2.5% What is the Sharpe ratio of the portfolio? .635% .333% .788% .838% .425%

.788%

Assume the returns on Stock X were positive in January, February, April, July, and November. During the other months, the returns on Stock X were negative. The returns on Stock Y were positive in January, April, May, July, August, and October, and negative the remaining months. Which one of the following correlation coefficients best describes the relationship between Stock X and Stock Y? −.5 .5 1.0 0 −1.0

0

Stock A has a standard deviation of 15% per year and Stock B has a standard deviation of 21% per year. The correlation between Stock A and Stock B is .30. You have a portfolio of these two stocks wherein Stock B has a portfolio weight of 60%. What is your portfolio standard deviation? 15.50% 16.91% 14.87% 18.03% 17.45%

15.50 VarPort = [(.40)^2 × .15^2] + [.60^2 × .21^2] + [2 × (.40) × .60 × .15 × .21 × .30] = .02401 Std DevPort = √.02401 = .1550, or 15.50%

A stock fund has a standard deviation of 18% and a bond fund has a standard deviation of 10%. The correlation of the two funds is .15. What is the approximate weight of the stock fund in the minimum variance portfolio? 20% 24% 11% 15% 27%

20% X*S = [.10^2 − (.18 × .10 × .15)]/[.18^2 + .10^2 − (2 × .18 × .10 × .15)] = .1973, or 19.73% (~20%)

Your portfolio has a standard deviation of 24.1%. What is the 2-year standard deviation? 39.48% 31.87% 36.55% 34.08% 41.15%

34.08% .241 × √2 = .3408

You have a portfolio which is comprised of 55% of Stock A and 45% of Stock B. What is the expected return on this portfolio? State of the Economy-Probability-E(RA)-E(RB) Weight - - 55% 45% Boom .15 19% 12% Normal . .65 11% 7% Recession .20 −16%. 1% 5.45% 7.14% 7.60% 6.69% 8.22%

6.69%

Six years ago, you purchased 210.20 shares of a mutual fund. Since then, you have reinvested your fund dividends and acquired an additional 36.32 shares. The fund currently has an NAV of $38.95. The fund charges a contingent deferred sales charge of 5% for the first 2 years after which time the charge declines by 1% a year. How much money will you receive if you redeem all your shares today? $9,699.79 $9,603.75 $9,414.52 $9,505.93 $9,320.38

Cash from redemption = (210.20 + 36.32) × $38.95 × (1 − .01) = $9,505.93

Five years ago, you purchased 220.80 shares of a mutual fund. Since then, you have reinvested your fund dividends and acquired an additional 35.10 shares. The fund currently has an NAV of $37.60. The fund charges a contingent deferred sales charge of 5% for the first 2 years after which time the charge declines by 1% a year. How much money will you receive if you redeem all your shares today? $9,360.32 $9,510.18 $9,429.40 $9,633.75 $9,700.79

Cash from redemption = (220.80 + 35.10) × $37.60 × (1 − .02) = $9,429.40

What is the standard deviation of the returns on this stock? State of the Economy Probability E(R) Boom .22 24% Normal .66 12% Recession .12 −60% 24.17% 26.90% 24.08% 24.85% 223.94%

E(R) = (.22 × 24%) + (.66 × 12%) + (.12 × −60%) = 6.00% Var = .22(24% − 6%)^2 + .66(12% − 6%)^2 + .12(−60% − 6%)^2 = 617.76% Std Dev = √617.76% = 24.85%

What is the variance of the expected returns on this stock? State of Econ. Probability. Rate of Ret Boom .40 15% Normal .60 19% 1.42% 1.56% 3.84% 1.21% 4.03%

E(R) = (.40 × 15%) + (.60 × 19%) = 17.4% Var = .40(15% − 17.4%)^2+ .60(19% − 17.4%)^2 = 3.84%

You have a portfolio which is comprised of 30% of Stock A and 70% of Stock B. What is the portfolio standard deviation? State of the Economy. Probability. E(RA). E(RB) 30% 70% Boom .15 20%. 14% Normal .75 11% 9% Recession .10 −23% −5% 6.82% 5.56% 4.00% 7.47% 6.68%

E(RBoom) = (.30 × 20%) + (.70 × 14%) = 15.80% E(RNormal) = (.30 × 11%) + (.70 × 9%) = 9.60% E(RRecession) = (.30 × −23%) + (.70 × −5%) = −10.40% E(RPortfolio) = (.15 × 15.80%) + (.75 × 9.60%) + (.10 × −10.40%) = 8.53% VarPortfolio = .15(15.8% − 8.53%)^2 + .75(9.6% − 8.53%)^2 + .10(−10.4% − 8.53%)^2 = 44.62% Std DevPortfolio = √41.05% = 6.68%

You have a portfolio which is comprised of 40% of Stock A and 60% of Stock B. What is the standard deviation of this portfolio? State of the Economy Probability A B Boom .15 22% 19% Normal. .80 12% 10% Recession. .05 −26% −4% 5.68% 6.41% 7.14% 4.39% 9.08%

E(RBoom) = (.40 × 22%) + (.60 × 19%) = 20.20% E(RNormal) = (.40 × 12%) + (.60 × 10%) = 10.80% E(RRecession) = (.40 × −26%) + (.60 × −4%) = −12.80% E(RPortfolio) = (.15 × 20.20%) + (.80 × 10.80%) + (.05 × −12.80%) = 11.03% VarPortfolio = .15(20.20% − 11.03%)^2 + .80(10.8% − 11.03%)^2 + .05(−12.80% − 11.03%)^2 = 41.05% Std DevPortfolio = √41.05% = 6.41%

The U.S. Treasury bill is yielding 1.5% and the market has an expected return of 10.2%. What is the Sharpe ratio of a portfolio that has a beta of 1.32 and a variance of .0323? .826 .639 .743 .573 .550

E(RP) = 1.5% + 1.32(10.2% − 1.5%) = 12.98% Sharpe ratio = (.1298 − .015) / √.0323 = .639

The Stable Utility Fund has an offering price of $54.11 and an NAV of $52.48. What is the front-end load percentage? 3.1% 3.0% 3.5% 4.0% 3.8%

Front-end load = ($54.11 − $52.48) / $54.11 = .030, or 3.0%

Which of the following are affected by the probability of a state of the economy occurring? I. expected return of an individual security II. expected return of a portfolio III. standard deviation of an individual security IV. standard deviation of a portfolio

I, II, III, and IV

Which of the following can you do with an ETF that you cannot do with an open-end fund? I. sell at mid-day prices II. short sell III. buy options on them IV. resell

I, II, and III only

A fund has an alpha of .89% and a tracking error of 3.8%. What is the fund's information ratio? .149 .212 .135 .234 .112

Information ratio = .89 / 3.8 = .234

Which one of the following statements is correct concerning an open-end mutual fund which charges a front-end load? If an investor wishes to sell her shares, she must do so by selling to another investor. The NAV exceeds the offering price. Investors receive the NAV when shares are sold. The load is expressed as a percentage of the NAV The number of shares outstanding was fixed at the time the fund was created.

Investors receive the NAV when shares are sold.

Your portfolio actually earned 4.39% for the year. You were expecting to earn 6.27% based on the CAPM formula. What is Jensen's alpha if the portfolio standard deviation is 12.1% and the beta is .99?

Jensen's alpha = 4.39% − 6.27% = − 1.88%

Your portfolio has a standard deviation of 12.3% and an average return of 9.6%. You have a 5% probability of losing ________% or more in any given year. Prob of Loss. "z" value 1% 2.326 2.5 1.960 5 1.645 31.54 10.63 3.34 12.59 33.79

Loss% = .096 − 1.645 (.123) = −.1063, or −10.63%

A portfolio has a standard deviation of 15.8% and an average return of 14.2%. What loss is associated with a 2.5% probability? Probability of loss "z" value 1.0% 2.326 2.5 1.960 5.0 1.645

Loss% = .142 − 1.96(.158) = −.1677, or −16.77%

A mutual fund has a current offering price of $35.70. What is the net asset value if the fund charges a 3.75% front-end load? $34.91 $34.86 $34.36 $31.66 $30.74

NAV = $35.70 × (1 − .0375) = $34.36

The Stone Wall Fund has an offer price of $43.20 and a front-end load of 2.5%. What is the net asset value? $45.05 $42.12 $43.90 $42.75 $42.83

NAV = $43.20 × (1 − .025) = $42.12

A mutual fund has a current offering price of $56.70. What is the net asset value if the fund charges a 4.5% front-end load? $54.15 $54.86 $51.66 $54.91 $50.74

NAV = $56.70 × (1 − .045) = $54.15

The Liberty Fund has an offer price of $57.32 per share and a front-end load of 2.25%. What is the net asset value? $57.03 $57.32 $56.03 $58.61 $56.34

NAV = $57.32 × (1 − .0225) = $56.03

At the beginning of the year, you invested $5,000 in a no-load mutual fund with a NAV of $25.00. At the end of the year, the fund distributed $1.10 per share in short-term earnings and $3.10 per share in long-term earnings. The end-of-year NAV was $24.60. What was your annual rate of return on this investment? 11.80% −1.86% −5.90% 17.90% 15.20%

Number of shares = $5,000 / $25.00 = 200.00 Return = [200 × ($1.10 + $3.10 + $24.60) − $5,000] / $5,000 = .1520, or 15.20%

You invested $7,000 in a mutual fund 28 months ago when the NAV of the fund was $22.30. You have not acquired or sold any shares since that time. Today, the NAV is $21.50. The fund charges contingent deferred sales charges of 6%, 5%, 4%, 3%, 2%, 2%, and 1% if the shares are redeemed within the first 7 years, respectively. How much money will you receive if you redeem your shares today? $6,478.92 $6,355.00 $6,275.23 $6,178.86 $6,508.91

Number of shares purchased = $7,000 / $22.30 = 313.90 shares Cash from redemption = 313.90 × $21.50 × (1 − .04) = $6,478.92

The High Growth Technology Fund has an NAV of $37.23 and a 2.4% front-end load. What is the offering price? $36.53 $34.84 $35.36 $38.15 $36.34

Offering price = $37.23 / (1 − .024) = $38.15

The High Yield Money Market Fund returned 6.60% for the last year. Currently, you own 8,901.1 shares of this fund. If you invested in this fund one year ago, what was the amount of your original investment? $8,402.38 $9,650.03 $8,682.51 $8,750.00 $8,350.00

Original investment = 8,901.1 / (1 + .066) × $1 = $8,350.00

Which one of the following correctly states the VaR for a 3-year period with a 2.5% probability? Prob[Rp,T ≤ E(Rp) × √3 − 1.645 × σp 3] Prob[Rp,T ≤ E(Rp) × 3 − 1.960 × σp √3] Prob[Rp,T ≤ E(Rp) × 3 − 1.645 × σp √3] Prob[Rp,T ≤ E(Rp) × √3 − 1.960 × σp 3] Prob[Rp,T ≤ E(Rp) × √3 − 1.645 × σp √3]

Prob[Rp,T ≤ E(Rp) × 3 − 1.960 × σp √3]

You want to buy 1,200 shares of a mutual fund that has an NAV of $27.80. The fund charges a 3.75% front-end load. How much will you have to spend to make this purchase? $36,953.37 $37,333.33 $38,445.60 $35,913.00 $34,659.74

Purchase cost = 1,200 × [$27.80 / (1 − .0375)] = $34,659.74

One year ago, Allison purchased 350 shares of a mutual fund which has a front-end load of 5.25%. The NAV at the time of purchase was $31. Today, the NAV is $34. The fund had total annual expenses of 1.65%. There were no fund distributions this past year. What is Allison's rate of return for the year? 4.76% −1.10% 3.92% 5.00% 4.23%

Purchase price = $31 / (1 − .0525) = $32.72 Rate of return = ($34 − $32.72) / $32.72 = .0392, or 3.92%

Five months ago, you purchased 200 shares of a mutual fund at an offering price of $54 a share. The fund imposes a front-end load of 4.5% and has total annual expenses of 1.08%. The NAV of the fund today is $52.40. There were no fund distributions during these five months. What is your holding period return on this investment? 1.44% 1.89% −1.92% −2.96% 2.26%

Rate of return = ($52.40 − $54) / $54 = −.0296, or −2.96%

Clark purchased 227 shares of a mutual fund with an offering price and NAV of $35.03 per share a year ago. Today, the NAV is $33.52 per share and the fund has just distributed $3.23 per share in long-term gains. What is Clark's rate of return? 4.91% 14.29% 5.13% 13.53% −4.31%

Return = ($33.52 + $3.23 − $35.03) / $35.03 = .0491, or 4.91%

A portfolio has a beta of 1.23 and a standard deviation of 11.6%. What is the Sharpe ratio if the market return is 12.4% and the market risk premium is 7.9%? .118 .902 .838 .073 .655

Risk-free rate = 12.4% − 7.9% = 4.5% E(RP) = 4.5% + 1.23(7.9%) = 14.2% Sharpe ratio = (.142 − .045) / .116 = .838

A portfolio consists of the following two funds: Fund A Fund B $ Invested $10,000 $15,000 Weight 40% 60% Exp Return. 14% 12% Std Dev 25% 15% Beta 1.92 1.27 Corr(A,B) 0.28 Riskfree rate 2.95% What is the Sharpe ratio of the portfolios? .547 .648 .721 .798 .422

Sharpe Ratio = [(.40 × .14) + (.60 × .12)] − .0295 / √(.4^2 × .25^2) + (.6^2 × .15^2) + 2(.4)(.6)(.25)(.15)(.28)= .648

A portfolio has an expected annual return of 12.2% and a standard deviation of 18.2%. What is the smallest expected loss over the next calendar quarter given a probability of 1%? 16.55% 17.25% 18.87% 18.12% 17.49%

Smallest loss = (.122 × .25) − 2.326 × (.182 × √.25) = −.1812, or −18.12%

Trailer Co. stock has an expected return of 12.2% and a standard deviation of 11.8%. What is the smallest expected loss over the next month given a probability of 5%? 7.27% 6.09% 11.49% 4.59% 13.77%

Smallest loss = (.122 × 1 / 12) − 1.645 × [.118 × √(1 / 12)] = −.0459, or −4.59%

High Mountain Homes has an expected annual return of 16.1% and a standard deviation of 20.3%. What is the smallest expected loss over the next month given a probability of 2.5%? 10.14% 6.64% 15.13% 12.12% 8.67%

Smallest loss = (.161 × 1 / 12) − 1.96 × [.203 × √ (1 / 12)] = −10.14%

You currently have a portfolio comprised of 70% stocks and 30% bonds. Which one of the following must be true if you change the asset allocation? The revised portfolio will be perfectly negatively correlated with the initial portfolio. The expected return will remain constant. The portfolio variance will most likely decrease in value. The portfolio variance will be unaffected. The two portfolios could have significantly different standard deviations.

The two portfolios could have significantly different standard deviations.

Which one of the following statements about efficient portfolios is correct? An efficient portfolio will have the lowest standard deviation of any portfolio consisting of the same two securities. Any efficient portfolio will lie below the minimum variance portfolio when the expected portfolio return is plotted against the portfolio standard deviation. There are multiple efficient portfolios that can be constructed using the same two securities. Any portfolio mix consisting of only two securities will be an efficient portfolio. There is only one efficient portfolio that can be constructed using two securities.

There are multiple efficient portfolios that can be constructed using the same two securities.

Which one of the following statements about efficient portfolios is correct? There is only one efficient portfolio that can be constructed using two securities. Any efficient portfolio will lie below the minimum variance portfolio when the expected portfolio return is plotted against the portfolio standard deviation. There are multiple efficient portfolios that can be constructed using the same two securities. Any portfolio mix consisting of only two securities will be an efficient portfolio. An efficient portfolio will have the lowest standard deviation of any portfolio consisting of the same two securities.

There are multiple efficient portfolios that can be constructed using the same two securities.

Which one of the following statements is correct concerning asset allocation? There is an ideal asset allocation between stocks and bonds given a specified level of risk. Because there is an ideal mix, all investors should use the same asset allocation for their portfolios. Asset allocation should play a minor role in portfolio construction. Asset allocation affects the expected return but not the risk level of a portfolio. The minimum variance portfolio will have a 50/50 asset allocation between stocks and bonds.

There is an ideal asset allocation between stocks and bonds given a specified level of risk.

What is the Treynor ratio of a portfolio comprised of 45% Portfolio A and 55% Portfolio B? A B Weight 45%. 55% Avg Return. 13.60%. 8.40% Std Dev 17.20% 6.40% Beta 1.38 0.87 The risk-free rate is 3.12% and the market risk premium is 8.5%. .114 .136 .058 .069 .041

Treynor Ratio=[(.45×.136)+(.55×.084)]−.0312(.45×1.38)+(.55×.87)=.069

Which one of the following is computed by dividing a portfolio's risk premium by the portfolio beta? Value-at-Risk raw return Treynor ratio Jensen's alpha Sharpe ratio

Treynor ratio

Which one of the following measures risk premium in relation to systematic risk? beta Sharpe ratio Value-at-Risk Treynor ratio Jensen's alpha

Treynor ratio

Your portfolio has a beta of 1.05, a standard deviation of 14.3%, and an expected return of 14.5%. The market return is 11.3% and the risk-free rate is 3.1%. What is the Treynor ratio?

Treynor ratio = (.145 − .031) / 1.05 = .109

What is the Treynor ratio of a portfolio comprised of 40% Portfolio A, 25% Portfolio B, and the risk-free rate is 2.5% and the market risk premium is 8.4%. Asset Weight. Avg Return. Std Dev. Beta A 40% 15.30% 17.20% 1.25 B 25% 10.50%. 9.80% 1.3 C 35% 13.30% 14.10% 0.95 .081 .076 .094 .063 .057

Treynor ratio = [(.40 × .153) + (.25 × .105) + (.35 × .133) − .025]/[(.40 × 1.25) + (.25 × 1.30) + (.35 × .95)] = .09417

The Aggressive Eastern Fund sold $278 million of assets during the year and purchased $295 million of new assets. The average daily assets of the fund were $438 million. What is the turnover rate? 1.03 .65 .97 .67 .63

Turnover = $278 million / $438 million = .63

Trading symbols for mutual funds end in which letter? Q Z M X F

X

Contingent deferred sales charges: are no longer permissible. are applied only to front-end load funds. can be avoided. are applied at the time fund shares are purchased. are charged on an annual basis to cover distribution and marketing costs.

can be avoided.

As the number of individual stocks in a portfolio increases, the portfolio standard deviation: decreases at a constant rate. decreases at a diminishing rate. decreases at an increasing rate. remains unchanged. increases at a constant rate.

decreases at a diminishing rate.

Which one of the following is eliminated, or at least greatly reduced, by increasing the number of individual securities held in a portfolio? number of economic states market risk nondiversifiable risk various expected returns caused by changing economic states diversifiable risk

diversifiable risk

The Sharpe ratio is best used to evaluate which one of the following? diversified portfolios government bonds Treasury bills corporate bonds individual stocks

diversified portfolios

A fund that is basically an index fund that trades like a closed-end fund is called a(n): exchange-traded fund. money market fund. open-end fund. depository receipt. mutual fund.

exchange-traded fund.

Which one of the following returns is the average return you expect to earn in the future on a risky asset? real return realized return expected return adjusted return market return

expected return

Which one of the following types of funds is most apt to invest in preferred stocks? balanced income index insured world

income

Mutual fund trading costs: increase in direct relation to the turnover rate are computed as a percentage of a fund's assets. generally include a bonus fee for outperforming an index. are generally set at a flat amount per year. are the costs paid to brokers in the form of sales commissions.

increase in direct relation to the turnover rate

You are graphing the investment opportunity set for a portfolio of two securities with the expected return on the vertical axis and the standard deviation on the horizontal axis. If the correlation coefficient of the two securities is +1, the opportunity set will appear as which one of the following shapes? hyperbole horizontal line conical shape linear with an upward slope combination of two straight lines

linear with an upward slope

Which of the following are three key advantages of mutual funds? professional management, high initial investments, taxes diversification, taxes, high initial investments liquidity, high initial investments, diversification costs, diversification, liquidity low initial investments, professional management, diversification

low initial investments, professional management, diversification

You have computed the expected return using VaR with a 2.5% probability for a 1-year period. How would this expected return be expressed on a normal distribution curve? the point that corresponds to 2.5 standard deviations below the mean the negative range that lies within 2.5 standard deviations of the mean the point that represents the lower end of the 90% probability range lower tail starting at the point that is 2.5 standard deviations below the mean lower tail of a 95% probability range

lower tail of a 95% probability range

A group of stocks and bonds held by an investor is called which one of the following? bundle portfolio grouping basket weights

portfolio

What are the two best reasons for considering a load fund? preference for a particular fund manager or a specialized type of fund tax-free income and superior fund managers superior market performance and preferential tax treatment no management fees and a particular fund manager lack of good no-load funds and superior market performance

preference for a particular fund manager or a specialized type of fund

The principal of diversification involves investing in a variety of assets with which one of the following being the primary goal? reducing some of the risk increasing returns minimizing taxes eliminating all of the risk increasing the variance

reducing some of the risk

A 12b-1 fee is a fee charged by a mutual fund: at the time shares are issued. to cover trading costs. to pay the fund's managers. if shares are sold within a stated period of time. to cover marketing costs.

to cover marketing costs.

The value of an individual security divided by the total value of the portfolio is referred to as the portfolio: variance. standard deviation. balance. beta. weight.

weight