F303 Exam 1 - Chapter 1&2

Scenario 3: Consider the following limit order book for FinTrade stock. The last trade in the stock occurred at a price of $150. Limit Buy orders | Limit Sell orders price, shares, price, shares $149.75, 500, $149.80, 100 $149.70, 800, $149.85, 100 $149.65, 500, $149.90, 100 $149.60, 200, $149.95, 100 $148.65, 600 If a market buy order for 100 shares comes in, at what price will it be filled? At what price would the next market buy order be filled?

$149.80 $149.85

Consider the following limit order book. The last trade in the stock occurred at a price of $40. If a market buy order for 100 shares comes in, at what price will it be filled? Limit buy price, order shares, limit sell orders, order shares $39.75, 100, $40.25, 100 $39.50, 100, $40.50, 100

$40.25

A T-bill quote sheet has 90 day T-bill quotes with 4.92 ask and 4.86 bid. If the bill has a $10,000 face value, an investor could sell this bill for ____. Assume 360 days

(1-[(.0486*90)/360])*10,000=9879

Scenario 2: Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. P0, Q0, P1, Q1 A 93, 100, 98, 100 B 53, 200, 48, 200 C 106, 200, 116, 200 Calculate the rate of return on a market value weighted index of the three stocks for the first period t=0 to t=1. Calculate the rate of return on an equally weighted index of the three stocks for the first period t=0 to t=1.

(93*100)+(53*200)+(106*200)=41,000 (98*100)+(48*200)+(116*200)=42,6000 (42,600-41,000)/41,000=3.65% (98-93)/93=5.38% (48-53)/53=-9.43% (116-106)/106=9.43% (5.38%+-9.43%+9.43%)/3=1.79%

An investor buys a T-Bill at a bank discount quote of 6.20 with 180 days to maturity. The bill has a face value of $10,000. The investors return adjusted for 365 days (bond equivalent yield) on this investment is ____. (assume 360 days for the price quote)

0.062*(180/360)=0.031 10000*(1-.031)=9690 ((10000-9690)/9690)*(365/180)=6.49%

Scenario 2: Assume that you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 36%. The T-bill rate is 6%. Your client chooses to invest 80% of a portfolio in your fund and 20% in a T-bill money market fund. What is the expected return? What is the and standard deviation of your client's portfolio? What is the reward-to-volatility ratio (S) of the risky portfolio?

10.8% 28.8% 16.67%

Barnegat Light sold 160,000 shares in an initial public offering. The underwriter's explicit fees were $62,000. The offering price for the shares was $32, but immediately upon issue, the share price jumped to $43. What is the best estimate of the total cost to Barnegat Light of the equity issue?

160,000*(43-32)+62,000=1,822,000

Security A has a higher standard deviation of returns than security B. We would expect that: 1. Security A would have a risk premium equal to security B. 2. The likely range of returns for security A in any given year would be higher than the likely range of returns for security B. 3. The Sharpe ratio of A will be higher than the Sharpe ratio of B.

2 only

Scenario 1: Dee Trader opens a brokerage account and purchases 200 shares of Internet Dreams at $44 per share. She borrows $4150 from her broker to help pay for the purchase. The interest rate on the loan is 10%. What is the margin in terms of $ amount in Dee's account when she first purchases the stock? If the share price falls to $34 per share by the end of the year and the maintenance margin requirement is 30%, will she receive a margin call? If the share price falls to $34, what is the rate of return on her investment?

44*200=8800 8800-4150=4650 34*200=6800 4150*(1+.1)=4565 6800-4565=2235 2235/6800=32.87% > 30% (2235-4650)/4650=-51.94%

You purchased 200 shares of ABC common stock on margin at $50 per share. The initial margin is 55% and the maintenance margin is 30%. Assuming the stock pays no dividends and there is no interest on the margin loan, at what price will you get a margin call?

50*(1-.55) = 22.5 22.5/(1-.3) = 32

The standard & poor's 500 is ___ weighted index.

A marke value

Scenario 1: The stock of Business Adventures sells for $60 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Dividend, Stock Price Boom $ 2.00 $ 70 Normal economy 1.80 63 Recession 0.90 54 Use Scenario 1: Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 5%.

HPR = 6.50%; STD = 11.68% 5.84%

NASDAQ Composite

Market value weighted index

NYSE Composite

Market value weighted index

Wilshire 5000

Market value weighted index

_____ portfolio construction starts with asset allocation

Top down

Which risk can be partially or fully diversified away as additional securities are added to a portfolio? I. Total risk II. Systematic risk III. Firm-specific risk

Total risk and Firm specific risk

After considering current markets, there should be a risk-return trade off with higher risk assets having ___ expected returns than lower risk assets.

higher

Both investors and gamblers take on risk. The difference between an investor and a gambler is that an investor __________.

requires a risk premium to take on the risk

If an investor places a ___ order, the stock will be sold if its price falls to the stipulated level. If an investor places a ___ order, the stock will be bought if its price rises above the stipulated level.

stop-loss, buy-stop

Initial margin requirements on stocks are set by __.

the Federal reserve

security selection decision:

the choice of which particular securities to hold within each asset class

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bull money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected return, standard deviation Stock fund: 16%, 40% Bond fund: 10%, 31% The correlation between the fund returns is 0.12 What is the expected return and standard deviation for the minimum variance portfolio of the two risky funds?

𝐸(𝑅min) = 12.5% ; 𝜎min, = 25.88%

Scenario 2: A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 15% 34% Bond fund (B) 9% 25% The correlation between the fund returns is 0.13. Your optimal risky portfolio consists of 64.94% in stock fund and 35.06% in bond fund. Suppose now that your complete portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL. What is the standard deviation of your complete portfolio? What is the proportion invest in the T-bill fund? What is the proportion invested in the Stock fund?

𝟐𝟏.𝟕𝟖% 12.16% 57.04%

You sell short 300 shares of Alpha Corp. that are currently selling at $30 per share. You post the 50% margin required on the short sale. If you earn no interest on the funds in your margin account, what will be your rate of return after 1 year if Alpha Corp. is selling at $27?

300*30=9000 9000*.5=4500 9000+4500=13,500 300*27=8100 13500-8100=5400 (5400-4500)/4500=20%

You are considering investing $1,100 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 15%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 7%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y, respectively.

33%; 20%; 13%

You are bearing on Telecom and decide to short sell 100 shares at the current market price of $35 per share. How high can the price of the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position?

35*100=3500 3500*.5=1750 3500+1750=5250 (5250-100p)/100p=<.3 p=40.38

Scenario 3: A portfolio earned a rate of return equal to 9.9% last year with a standard deviation of 16.0%. Treasury Bills returned 1.4%. What's the portfolio's excess return? What is the portfolio's Sharpe Ratio?

8.50% .53

You are provided with an endowment for portfolio allocation. You need to allocate between three asset categories, riskless asset, US stock market, and venture capital (which is not part of the US stock market). You have estimated the following based on annual data: The riskless rate is 6% and the correlation between US stocks and VC is 0.30. Based on this, optimal risky portfolio (tangency portfolio) is 60% in US stocks and 40% in VC. US stocks has an expected return of 25% and a standard deviation of 40%. Venture capital has an expected return of 30% and a standard deviation of 50%. What is the Sharpe ratio of the optimal risky portfolio? The endowment is for $100 million. It will accept a complete portfolio with a standard deviation of only 22%. How much should be invested in the VC fund? What expected return can endowment expect on this complete portfolio?

0.59 $24.8 million 18.99%

Three stocks have share prices of $33, $105, and $75 with total market values of $520 million, $470 million, and $270 million, respectively. If you were to construct a price-weighted index of the three stocks, what would be the index value?

(33+105+75)/3=71

Assume an investor with a risk aversion coefficient of 1.80. Historical evidence on the risky portfolio indicates that the average excess return has been around 8%. What is the standard deviation of the risky portfolio if the investor has invested 70% of her funds in the risky market portfolio?

25.20%

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 2%. The probability distributions of the risky funds are: Expected return, standard deviation stock fund: 12%, 28% bond fund: 6%, 16% The correlation between the fund returns is 0.25. Your optimal risky portfolio consists of 70% in stock fund and 30% in bond fund. Suppose now that your complete portfolio must yield an expected return of 14% and be efficient, that is, on the best feasible CAL. What is the standard deviation of your complete portfolio? How much is invested in the BOND fund and T-bill if pension fund manager is allocated a total endowment of $100,000?

𝟑𝟏.𝟏𝟗%. Invest $43,902 in the bond fund and borrow $46,340 at the risk free rate

The Dow Jones is a ___

price weighted index

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 3%. The probability distributions of the risky funds are: expected return, standard deviation stock fund: 8%, 30% bond fund: 5%, 20% The correlation between the fund returns is 0.6. What is the standard deviation for the minimum-variance portfolio of the two risky funds?

𝐸(𝑅min) = 5.21% ; 𝜎min = 19.92%

Today you would like to buy a risky portfolio and expect to generate cash flow of either $50,000 or $150,000 with equal probabilities at the end of the year from this risky portfolio. Suppose in the market, the risk premium is 10% and an investment in T-bills pay 5%. How much are you willing to pay for the portfolio today?

$86,957

Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t=0 to t=1).

(85+45+90)/3=73.33 (90+40+10)/3=76.66 (76.66-73.33)/73.33=4.55%

An investor's degree of risk aversion will determine his or her ______.

capital allocation line

an order to buy or sell a security at the current price is a __.

market order

You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 21% 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 an expected return of 11%?

$6,000

An investor purchases one municipal bond and one corporate bond that pay rates of return of 7% and 8.4%, respectively. If the investor is in the 15% tax bracket, his after-tax rates of return on the municipal and corporate bonds would be, respectively, _____.

7% & 7.14% (8.4%*15%)=7.14%

In the mean standard deviation graph, the line that connects the risk-free rate and the optimal risky portfolio, P, is called the __________.

capital allocation line

You have the following rates of return for a risky portfolio for several recent years. Assume that the stock pays no dividends. Year, Beginning of Year Price, # of Shares Bought or Sold 2016 $50 150 bought 2017 $55 100 bought 2018 $51 125 sold 2019 $54 125 sold What is the geometric average return for the period?

2.60%

Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global minimum-variance portfolio has a standard deviation that is always _________.

equal to zero

Scenario 1: A universe of securities includes two risky assets X & Y, and T-bills. The data for the universe are: Expected return(%) Standard deviation(%) X: 15, 50 Y: 7, 25 T-Bill: 5,0 The Correlation coefficient between X & Y is -0.2. The minimum variance portfolio has an expected return = 8.9%, standard deviation n= 20.3%. The optimal risky portfolio has weights: Wx=47.4%, Wy=52.6%. Given the weights of the optimal risky portfolio (O), find its expected return, standard deviation and Sharpe ratio. Find the slop of the CAL generated by T-bills and portfolio O Suppose an investor places 2/9 of the complete portfolio in the risky portfolio O and the remainder in T-bills. Calculate the composition of the complete portfolio, its expected return, standard deviation, and Sharpe ratio.

expected return: 𝟎.𝟎𝟔𝟏𝟎 standard dev: 𝟐𝟒.𝟕% Sharpe ratio: 𝟎.𝟐𝟑𝟓 0.235 Composition of complete portfolio: 7/9 = 77.8% in risk free asset 2/9 = 22.22% in optimal risky portfolio. Investment in X = 22.22% of 47.4% in X= 0.2222*0.474 = 0.105 = 10.5% Investment in Y = 22.22% of 52.6% in Y = 0.2222*0.526 = 0.117 = 11.7%

Some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is __.

less than 1

Two assets have the following expected returns and standard deviations when the risk-free rate is 5%: Asset A: E(RA) = 10%; σA = 20% Asset B: E(RB) = 15%; σB = 27% An investor with a risk aversion of A = 3 would find that __________ on a risk-return basis.

neither asset A nor asset B is acceptable

You manage an equity fund with an expected risk premium of 12.4% and a standard deviation of 38%. The rate on Treasury bills is 5.4%. Your client chooses to invest $120,000 of her portfolio in your equity fund and $80,000 in a T-bill money market fund. What are the expected return and standard deviation of your client's portfolio?

return = 12.84%; std = 22.80%

A project has a 0.54 chance of doubling your investment in a year and a 0.46 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment? The probability distribution is: Probability, rate of return .54, 100% .46, -50%

74.76%

asset allocation decision:

choice among broader asset classes such as stocks, bonds, real estate, commodities, etc.

security selection refers to the ___

choice of specific securities within each asset class

Which of the following is not a money market security? US T bill 6-month maturity certificate of deposit common stock commercial paper savings account

common stock

bottom-up portfolio

construction focuses on directly picking securities that seem attractively prices without much concern for asset allocation

top-down portfolio

construction starts with an asset allocation (what proportion of the portfolio will be stocks vs. bonds). then you decide on particular security to be held in each asset class

Scenario 3: You are provided with an endowment for portfolio allocation. You need to allocate between three asset categories, riskless asset, US stock market, and venture capital (which is not part of the US stock market). You have estimated the following based on annual data: The riskless rate is 6% and the correlation between US stocks and VC is 0.5. Based on this, optimal risky portfolio (tangency portfolio) is 70% in US stocks and 30% in VC. US stocks has an expected return of 16% and a standard deviation of 22%. Venture capital has an expected return of 21% and a standard deviation of 37%. What is the Sharpe ratio of the optimal risky portfolio? The endowment is for $100 million. It will accept a complete portfolio with a standard deviation of only 15%. How much should be invested in the stock fund? What expected return can endowment expect on this complete portfolio?

0.499 $45.5560 million 13.48%

Scenario 5: An investor, Samantha, is considering buying stock for ABC Corporation. It is currently selling for $80 with an annual divided of $2 per share. The stock price is expected to increase to $100 per share. The margin requirement set by the Federal Reserve is 60% and brokerage firms are charging 5% on funds used to purchase stock on margin. While commissions vary among brokers, you decide that $50 for a 100-share purchase or sale is a reasonable amount to use for your calculations. What is the percentage return earned by Samantha if she acquires 100 shares on margin (with an initial margin of 60%) at a price of $80 per share, holds the stock for a year, and sells the stock for $100? If the maintenance margin requirement were 30%, at what price of the stock will Samantha receive a margin call?

(100*80)+50=8050 (100*100)-50+(100*2)=10150 (10150-8050)/8050=26.09% 80*100=8000 8000*.4=3200 3200(1+0.05)+50=3410 (100*100)+(2*100)=10,200 10,200-3410=6790 8000*60%+50=4850 (6790-4850)/4850=40% ([100p+(2*100)]-[3200(1.05)+50])/(100p+(2*100))<=.3 p<=46.71

Scenario 1: A T-bill with face value $10,000 and 92 days to maturity is selling at a bank discount ask yield of 3.9%. What is the price of the bill? (use 360 days a year) What is the return adjusted for 365 days (bond equivalent yield)?

(92/360)*3.9%=.00996667 (1-.00996667)*10,000=9900 (365/92)*(10,000-9900/9900)=3.99%

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return, Standard Deviation Stock fund: 16%, 34% Bond fund: 10%, 25% The correlation between the fund returns is 0.11. If the optimal risky portfolio proportions are Ws = 59.27% and Wb = 40.73%, what is the Sharpe ratio of the best feasible CAL?

0.3421

You manage an equity fund with an expected risk premium of 14% and a standard deviation of 54%. The rate on Treasury bills is 6.8%. Your client chooses to invest $120,000 of her portfolio in your equity fund and $30,000 in a T-bill money market fund. What is the reward-to-volatility (Sharpe) ratio for the equity fund?

25.93%

You are provided with an endowment for portfolio allocation for $200 million. You need to allocate between three asset categories, riskless asset, US stock index, and corporate bond index. You have estimated the following based on annual data: The riskless rate is 9% and the correlation between US stocks and corporate bond market is 0.5. Based on this, optimal risky portfolio (tangency portfolio) is 53% in US stocks and 47% in corporate bonds. US stocks has an expected return of 18% and a standard deviation of 34%. Bond index has an expected return of 13% and a standard deviation of 19%. The endowment would like you to design a complete portfolio with an expected return of 20% and the smallest possible standard deviation. What standard deviation (in %) can the endowment expect on this complete portfolio?

39.33%

Scenario 4: You've borrowed $24,660 on margin to buy shares in Ixnay, which is now selling at $41.8 per share. You invest 1,180 shares. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price changes to $44 per share. Assume that you are paying 5% to the lender for the borrowed funds. What is your maintenance margin once the price increases to $44? How low can the price of the stock go before you get a margin call if the maintenance margin is 35%? What is the rate of return for the investor once the stock price increases to $44?

41.8*1180=49320 49320-24660=24660 24660(1+.05)=25893 44*1180=51920 51920-25893=26027 26027/51920=50.13% (1180p-25893)/1180p<=.35 p>=33.76 (26027-24660)/24660=5.54%

You invest $2,800 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 13% and a standard deviation of 20% and a Treasury bill with a rate of return of 8%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 12%.

60%

An investor is in a 40% combined federal plus state tax bracket. If corporate bonds offer 8.5% yields, what yields must municipals offer for the investor to be indifferent between corporate bonds and municipal bonds?

8.5%*(1-40%)=5.1%

Your uncle Bob has asked you for some financial advice. His retirement savings are currently invested as follows: 29% T-bills (i.e., risk-free asset) and 71% in ABC stocks. Let's suppose that the risk-free rate is 10% and the expected return on ABC stock is 𝐸(𝑅Q5R) = 16%. The standard deviation on ABC stock is 𝜎Q5R = 35%. You worry that your Uncle Bob' portfolio is not diversified enough. Instead, you offer him the following option: He can combine the T-bills (i.e., risk-free asset) and stock market index fund (i.e., M). If the expected return and the standard deviation of the index fund are 30% and 40% respectively, please construct your uncle a portfolio with T-bills and the index fund that offers the same return as his current portfolio. What is the standard deviation of your uncle's newly constructed complete portfolio's standard deviation?

8.52%

Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rƒ. The characteristics of two of the stocks are as follows: Stock Expected Return Standard Deviation A 7% 45% B 10% 55% Correlation = −1 What is the expected rate of return on a portfolio that is composed of stock A and stock B? (Hint: Can a particular stock portfolio be formed to create a "synthetic" risk-free asset?

8.53%

Scenario 2: Old Economy Traders opened an account to short-sell 1000 shares of Internet Dreams at $95 per share. The initial margin requirement was 50%. A year later, the price of the Internet Dreams has risen from $95 to $101, and the stock has paid a dividend of $15 per share. What is the remaining margin balance in the investor's account? If the maintenance margin requirement is 30%, will Old Economy receive a margin call? What is the rate of return on the investment?

95*1000 = 95000 95000*.5 = 47500 95000+47500=142500 1000*101=101000 142500-101000=41500 15*1000=15000 41500-15000=26500 26500/(101000+15000)=22.84% < 30% (26500-47500)/47500 = -44.21%

You have $500,000 available to invest in a complete portfolio. The risk-free rate, as well as your borrowing rate, is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return on your complete portfolio, you should __________.

borrow $375,000 at the risk-free rate and invest $875,000 in the risky asset