Exam 1 Study Guide

———————- portfolio construction starts with selecting attractively priced securities. (a) Bottom-up (b) Top-down (c) Upside-down (d) Side-to-side (e) Right-side up

(a) Bottom-up

4. (5 points) You just caught wind that Facebook paid $19 billion for a texting app. In your opinion, there are two main negatives about this purchase. First, you believe they significantly overpaid. Second, you think this shows Facebook doesn't know how to wisely invest their money and will struggle to produce lasting growth in the future. As a result of your pessimistic viewpoint, you decide to short sell 400 shares of Facebook stock at the current price of $69.63. (a) (2 points) If the initial margin is 75%, how much must you deposit with your broker as collateral? (b) (3 points) Suppose you were correct and the price of Facebook stock has fallen to $66.78 (although its stock seems to be fairly resilient). What was the rate of return on your investment (assume that you earn no interest on the collateral that you deposited and there are no dividends)?

(a) Shorting 400 shares of Facebook results in a total of 400(69.63) = 27, 852 deposited to your account. A 75% margin means you must deposit an additional 0.75(27, 852) = 20, 889 into your account as collateral. (b)The price fell by 69.63 − 66.78 = 2.85. This means that you made $2.85 on each share that you shorted. Your return is then r =2.85(400)/20, 889 = 0.0546 or 5.46%

15. (6 points) Suppose you invested $20,000 two years ago. $10,000 was invested into a mutual fund that has a 3% front-load, a 1.75% 12-1b fee, and a 1% back-load. The other $10,000 was invested in a no-load mutual fund with an annual fee of 0.25%. Over the past two years, the load-fund (first one) averaged an annual return of 16% and the no-load fund averaged a 13% annual return. (a) (2 points) How much money did you end up with in the load fund? (b) (2 points) How much money did you end up with in the no-load fund? (c) (2 points) Which fund performed better over the 2 year horizon? Would your answer change if we looked at a 10-year horizon (assuming everything remains the same)? (No need to recalculate, simply explain the intuition).

(a) Solution: load fund = initial investment(1-front-load)[(1- annual return) - 12-1lb fee^2)](1-back-load) 10, 000(0.97)(1.16 − 0.0175)^2 (0.99) = 12, 534.86 (b)Solution: no-load= initial investment (annual return-annual fee)^2 10, 000(1.13 − 0.0025)^2 = 12, 712.56 (c) Solution: Once we reach an investment horizon of 5 years (and beyond), the higher annual return generated by the load fund more than offsets the higher fees. Specifically, you would have 10, 000(0.97)(1.16 − 0.0175)^5(0.99) = 18, 693.39 after 5 years in the load fund versus only 10, 000(1.13−0.0025^)5 = 18, 221.44 from the no-load fund. This difference will only get larger as we increase the investment horizon.

6. The most marketable money market security is

(a) Treasury bills

Consider a mutual fund that invests primarily in fixed-income securities. Which of the following is least likely to be included in the fund? (a) Warrants (b) Commercial Paper (c) Treasury bills (d) Repurchase agreements (repos)

(a) Warrants

The slope of the security characteristic line —————— (a) measures the average response of an individual security's return to changes in the market return (b) cannot be negative (c) is a measure of the security's firm-specific risk (d) all of the statements about the security characteristic line are correct

(a) measures the average response of an individual security's return to changes in the market return

The primary measurement unit used for assessing the value of one's stake in an investment company is ———————-

(a) net asset value

8. The risk that can be elinated by diversification is called —————- risk, while the risk that remains even after diversification is called ——————— risk.

(a) nonsystematic; market

5. When computing the bank discount yield, you would use ——- days in the year.

(b) 360

Individuals may find it more advantageous to purchase claims from a financial intermediary rather than directly purchasing claims in capital markets because: I. Intermediaries are better diversified than most individuals II. Intermediaries can exploit economies of scale in investing that individual investors cannot III. Intermediated investments usually offer higher rates of return than direct capital market claims

(b) I and II only

8. An investor purchases one municipal bond and one corporate bond that pay rates of return of 5% and 6.4%, 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

(b) Muni is 5% after-tax since it is tax-free. For the other, it is simply r = 0.064(1 − 0.15) = 5.44%

Which of the following statements about exchange-traded funds (ETFs) is most correct? (a) Exchange-traded funds are not backed by any assets. (b) The investment companies that create exchange-traded funds are financial intermediaries. (c) The transaction costs of trading shares of exchange-traded funds are substantially greater than the combined costs of trading the underlying assets of the fund. (d) The annual fees are typically higher for an ETF than an actively managed mutual fund. (e) Shares of ETFs trade only at the closing value.

(b) The investment companies that create exchange-traded funds are financial intermediaries.

In calculating the Dow Jones Industrial Average, the adjustment for a stock split occurs (a) automatically (b) by adjusting the divisor (c) by adjusting the numerator (d) by adjusting the market value weights (e) there is no adjustment. Stock splits affect the Dow since it is price-weighted

(b) by adjusting the divisor

You are considering investing in one of several mutual funds. All the funds under consideration have various combinations of front-end and back-end loads and/or 12b-1 fees. The longer you plan on remaining in the fund you choose, the more likely you will prefer a fund with a ——————- rather than a ——————-, everything else equal. (a) 12b-1 fee; front-end load (b) front-end load; 12b-1 fee (c) back-end load; front-end load (d) 12b-1 fee; back-end load

(b) front-end load; 12b-1 fee

11. The investment opportunity set is ———————— (a) equivalent to the efficient frontier (b) the set of all available portfolio risk-return combinations (c) the set of portfolios that minimize risk for a given expected rate of return (d) the set of portfolios ideal to the investor in question

(b) the set of all available portfolio risk-return combinations

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

(b). The quoted ask is a bank discount yield. This means rBD = [(Par − P)/ Par] x (360/n) Plugging in the information from the problem, we get 0.0486 = [(10, 000 − P)/10, 000] (360/90) Solving this for the ask price, P, we get P = 9, 878.50

9. John Mathew has a $800,000 fully diversified portfolio. He subsequently inherits XYZ company common stock worth $200,000. His financial adviser provided him with the following estimates: The original portfolio has expected monthly returns of 0.34%, and standard deviation of monthly returns of 1.19%. XYZ Company has expected monthly returns of 0.63% and standard deviation of monthly returns of 1.48%.The correlation coefficient of XYZ stock returns with the original portfolio returns is .20. The inheritance changes Mathew's overall portfolio, and he is deciding whether to keep the XYZ stock. Assuming Mathew keeps the XYZ stock, calculate the standard deviation of his new portfolio which includes the XYZ stock.

(b). The standard deviation is simply the square root of the variance. The variance of the portfolio is σ^2new = w^2Aσ^2A + w^2Bσ^2B + 2ρABwAwBσAσB Plugging everything in we get σA= .0.0119 σB= .0.0148 ρ=0.2 wA= .8 wB=.2 σ^2new = (0.8)^2(0.0119)^2 + (0.2)^2(0.0148)^2 + 2(0.2)(0.8)(0.2)(0.0119)(0.0148) = 0.00011 σnew =√0.00011 = 0.01052

5. A portfolio is composed of two stocks, A and B. For Stock A, the standard deviation of the rate of return is 20%. For Stock B, the standard deviation of the rate of return is 30%. Stock A comprises 40% of the portfolio while Stock B comprises 60% of the portfolio. What is the standard deviation of return for the portfolio if the correlation coefficient between the returns for A and B is 0.5?

(b). The standard deviation is simply the square root of the variance. The variance of the portfolio is σ^2p = w^2Aσ^2A + w^2Bσ^2B + 2ρABwAwBσAσB Plugging in all of the information we get σA= .2 σB= .3 ρ=0.5 wA= .4 wB=.6 σ^2p = (0.4)^2(0.20)^2 + (0.6)^2 (0.3)^2 + 2(0.5)(0.4)(0.6)(0.2)(0.3) = 0.0532 σp =√0.0532 = 0.23065 ≈ 23.1%

15. You short-sell 200 shares of Rock Creek Fly Fishing Co., now selling for $50 per share. If you want to limit your loss to $2,500, you should place a stop-buy order at

(b). You want to limit your loss to $2500. Since you short-sold 200 shares, this means you want to limit your loss per share to 2500 200 = 12.50. When you short-sell a stock, you lose when the price increases. To limit your loss to $12.50 per share, you would want to place a stop-buy order at $50 + 12.50 = $62.50.

12. More than ——— of all trading is believed to bee initiated by computer algorithm. (a) 25% (b) 40% (c) 50% (d) 75% (e) 80%

(c) 50%

3. Which of the following is not a money market security? (a) U.S. Treasury bill (b) 6-month maturity certificate of deposit (c) Common stock (d) Bankers' acceptance

(c) Common stock

1. Active trading in markets and competition among securities analysts helps ensure that: I. Security prices approach informational efficiency II. Riskier securities are priced to offer lower potential returns III. Investors are unlikely to be able to consistently find under- or overvalued securities

(c) I and III only

4. Which of the following is not a financial intermediary? (a) a mutual fund (b) an insurance company (c) a real estate brokerage firm (d) a savings and loan company

(c) a real estate brokerage firm

Which of the following is not a financial intermediary? (a) a mutual fund (b) an insurance company (c) a real estate brokerage firm (d) a savings and loan company (e) these are all examples of financial intermediaries

(c) a real estate brokerage firm

In an underwritten offering (such as your typical IPO), the risk that the entire issue may not be sold to the public at the stipulated offering price is borne by the: (a) issuer (b) investors in the newly issued asset (c) investment bank (d) FDIC which federally guarantees these transactions

(c) investment bank

Portfolio diversification benefits ————— (a) exist only when security returns are negatively correlated (b) are always available, regardless of securities' correlation coefficients (c) exist whenever security returns are less than perfectly positively correlated (d) are greater for positively correlated security returns than for negatively correlated security returns

(c). Anything less than perfect positive correlation will yield benefits to diversification (i.e. reduce the risk by combining assets).

The material wealth of society is determined by the economy's ———————-, which is a function of the economy's —————-.

(d) productive capacity; real assets

Adding additional risky assets to the investment opportunity set will generally move the efficient frontier —————- and to the —————-. (a) down; right (b) down; left (c) up; right (d) up; left (e) no shift

(d) up; left

10. The Hydro Index is a price weighted stock index based on the 5 largest boat manufacturers in the nation. The stock prices for the five stocks are $10, $20, $80, $50 and $40. The price of the last stock was just split 2 for 1 and the stock price was halved from $40 to $20. What is the new divisor for a price weighted index?

(d). The original (before the split) value of a price weighted index was 10 + 20 + 80 + 50 + 40/5 = 40 After the stock split, we don't want the value of the index to change. This means we need to adjust the divisor so that the value of the index won't change even though the price of one stock has halved. 10 + 20 + 80 + 50 + 20/d = 40 Solving for d we get d = 4.5

Suppose you buy 200 shares at $50 a share on a 60% margin. The interest rate on the loan from your broker is 6% and the account has a 30% maintenance margin. In one year, you must pay interest and you get a margin call from your broker. At the time of the margin call, what was the price of the stock?

Buying 200 shares at $50 a share requires a total of 200(50) = $10, 000. The 60%margin means that you invested 10, 000(0.60) = $6, 000 and you borrowed 10, 000−6, 000 = $4000 from your broker. After one year, the total assets in the account (or value of the stock) is 200(P). You have both the liability of the loan and an interest payment of 4000(0.06) = 240. The equity in the account is simply the value of the stock minus any liabilities (loan and interest payments). The margin is the Equity/TA of the account. Thus,if we get a margin call 0.30 =(200P − 4000 − 240)/ 200P Solving this we get 60P = 200P − 4240 4240 = 140P P =4240/140= 30.29

The standard deviation of the rate of return for Stock A is 25%, and the standard deviation of the rate of return for Stock B is 30%. The covariance of the returns on Stock A and Stock B is 0.06. What is the correlation coefficient between the returns on Stock A and Stock B?

By definition ρAB =Cov(rA, rB)/(σAσB) ρAB =0.6/[(0.25)(0.30)] = 0.8

2. Compute the expected rate of return for the following two-stock portfolio: Stock E(r) Std. Dev. Weight A 18% 40% 0.7 B 12% 28% 0.3

E(rp) = wAE(rA) + wBE(rB) = 0.7(0.18) + 0.3(0.12) = 0.162

3. Suppose that two risky portfolios, Portfolio A and Portfolio B, are perfectly negatively correlated. Portfolio A has an expected rate of return of 10% and a standard deviation of the rate of return of 20%. Portfolio B has an expected rate of return of 12% and a standard deviation of the rate of return of 30%. Portfolio A and Portfolio B are combined in such a way that the combination has a standard deviation of zero. What is the weight of portfolio A?

P=-1 ; 1=wA+wB σ^2p = (wAσA − wBσB)^2 0 = (wAσA − (1 − wA)σB)^2 This implies 0 = wAσA − (1 − wA)σB Solving for wA, wA =σB/(σA + σB) =0.3/(0.2 + 0.3) = 0.6

6. Which of the following portfolios cannot lie on the efficient frontier? Stock E(r) Std. Dev. X 10% 15% Y 10% 25% Z 15% 25%

Portfolio Y cannot be on the efficient frontier because Portfolio X has the same expected return and a lower standard deviation

Suppose there are 3 assets in the economy, 1 is a risk-free asset and the other 2 assets (A and B) are risky. The risk-free rate is rf = 0.09. Asset A has an expected return of E[rA] = 0.06 and a standard deviation of σA = 0.10. Asset B has an expected return of E[rB] = 0.21 with a standard deviation of σB = 0.4. If assets A and B are perfectly negatively correlated, ρ = −1, find the expected return of the minimum variance portfolio (constructed using only assets A and B).

Since the two risky assets have a correlation of ρ = −1, the minimum variance portfolio will have a standard deviation of zero! Thus, it must have an expected return equal to the risk-free rate which is 0.09 or 9.00%. Solving this out mathematically will simply confirm our intuition.

Which of the following stocks is relatively more risky when held in a well-diversified portfolio? Stock Std. Dev. Beta ABC 30% 1.2 XYZ 40% 1.6 (a) XYZ because its beta is higher. (b) XYZ because its standard deviation is higher. (c) ABC because its beta is lower. (d) ABC because its standard deviation is lower

Solution: (a). When an asset is held in a well-diversified portfolio, the most appropriate risk measure is its beta (exposure to market/systematic risk

11. The margin requirement on a stock purchase is 25%. You fully use the margin allowed to purchase 100 shares of MSFT at $25. If the price drops to $22, what is your percentage loss?

Solution: (d) −48% The decrease in price by $3 causes a loss of 100(3) = $300. Our initial investment was 0.25(100)(25) = $625. Thus, the drop in the stock price led to a return of r =−300/625 = −0.48%

A bond issued by the state of Alabama is priced to yield 6.25%. If you are in the 28% tax bracket, this bond would provide you with an equivalent taxable yield of

The formula to find the equivalent taxable yield is req =r/(1 − t) where req is the equivalent taxable yield and r is the tax-free yield. Plugging in theappropriate values we get req =6.25/(1 − 0.28) = 8.68%

Even though your previous experience with buying on a margin didn't go as planned (no one likes getting a margin call), you decide to try again. You are positive that you have found a winning stock. It is currently worth $20 a share. You decide to purchase a total of $16,000 using an initial margin of 60%. This time, the broker charges you an interest of 8% on the loan. In one year, the stock pays a dividend of $0.50 and you sell all of your shares at $23 (phew, it feels good to pick a winner). What is your rate of return?

You purchased the $16,000 on a 60% margin which means you invested 16,000(60) =$9, 600 and you borrowed $6,400. #of sh = 16,000/20= 800 When you sell your shares for $23, you receive 23(800) =$18, 400. You also get 0.50(800) = $400 in dividends. This means you earned a total of 18,400 + 400 − 9, 600 = 9, 200 on your initial investment. but you need to payback your loan plus interest which comes to 6, 400(1.08) = $6, 912. Your final return is then r= [initial investment - borrowed(interest)]/initial investment r =(9, 200 − 6, 912)/9, 600 = 0.2833 or 23.83%

13. The bid-ask spread exists because of

the need for dealers to cover expenses and make a profit.

14. You short-sell 200 shares of Tuckerton Trading Co., now selling for $50 per share. What is your maximum possible loss?

unlimited