FINAL FIN 3710 SHEET

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School

Baruch College, CUNY *

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Course

3610

Subject

Finance

Date

Jan 9, 2024

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docx

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1

Uploaded by CoachDolphinPerson1012

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A municipal bond issued by the state of California is currently yielding 5.75%. If you are in the 25% tax bracket, what would be the equivalent taxable yield for this bond? 0.0575 / (1-0.25) *100 = R = 7.67% If the face value of a T-bill is $10,000, T-bill has 120-day and quotes with a 4.60 ask and a 4.55 bid. This T bill could sell for: $10,000 * (1-5.61% * (120/360)) = 9,813.00 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%? 11% = (15% * R) + (5% * (1-R)) R=60% 0.6 * 10000 = 6000 The risk-free rate is 10%. The return on the risky portfolio is 15%. The standard deviation of return on the risky portfolio is 20%. What is the expected return on the complete portfolio is if the standard deviation on the complete portfolio is 25%. 0 .25 / 0.20 = 1.25 (1 - 1.25) * .10 + 1.25 *0.15 = 0.1625 0.1625 * 100 = 16.25 Your firm invested $2,504,600 in 350-day commercial paper today. At the end of the investment period (in 350 days) the firm will receive $2,592,400. What is the 350-day holding period rate of return on the investment? The HPR equals (2,592,400 – 2,504,600) / 2,504,600 = 3.51%. What is the APR? (350/365*APR=3.51%) APR=365/350*3.51%=3.66% What is the effective annual rate (EAR)? (1 + 0.035) ^365/350 - 1= 1.0366-1, EAR = 3.66% David bought 250 shares of common stock on a margin of $25 per share. The stock does not pay dividends and the initial margin is 65%. If Marie sells the stock at $32 per share, what would be her rate of return? (25*250) – (25*250*0.35) = 4062.5 ((32-25)*250)/4062.5 = 43% You are evaluating an investment with three potential outcomes: Outcome A has a 40% probability and yields a 12% return. Outcome B has a 30% probability and yields a 5% return. Outcome C has a 30% probability and yields a -2% return. (0.40 * 0.12) + (0.30 * 0.05) + (0.30 * -0.02) =5.7% Suppose you pay $9,800 for a $10,000 par Treasury bill maturing in 2 months. What is the annual percentage rate of return for the investment? ($10,000 − $9,800)/$9,800 × 12/2 = 0.1224 = 12.24% Your investment has a 20% chance of earning a 30% rate of return, a 50% chance of earning a 10% rate of return, and a 30% chance of losing 6%. What is your expected return on this investment? (20%*30%) + (50%*10%) – (30%*6%) = 9.2% You short-sell 300 shares of Rock Creek Fly Fishing Company, now selling for $36 per share. If you want to limit your loss to $3,630, you should place a stop-buy order at ___. 300 × $36 = $10,800 $3,630 = 300 P − $10,800 $14,430 = 300 P , so P = $48.10 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 sell this bill for: P0 = $10,000 × (1−0.0486 × 90360) = $9,878.50 You purchased 200 shares of ABC common stock on margin at $50 per share. Assume the initial margin is 50% and the maintenance margin is 30%. You will get a margin call if the stock drops below: (200 × P − $5,000)/200 × P = 0.30, P=35.71 You purchased 600 shares of XYZ common stock on margin at $35 per share from a broker. If the initial margin is 60%, the amount borrowed from the broker is: 600($35) (0.40) = $8,400 An investor puts up $5,000 but borrows an equal amount of money from his broker to double the investment to $10,000. The broker charges 7% on the loan. The stock was originally purchased at $25 per share, and in 1 year the investor sells the stock for $28. The investor's rate of return was? Number of shares purchased: 10000/25=400 ((28-25) * 400-0.07*5000)/5000=0.17 Stock X has an expected return of 12% and a beta of 1. Stock Y has expected return of 13% and a beta of 1.5. The market return is 11% and riskfree rate is 5%. According to CAPM, which is a better buy? X: 5%+(11%-5%)*1=11% Alpha X: 12%-11%=1% Y: 5%+(11%-5%)*1.5=14% Alpha Y: 13%-14%=-1% If the expected market return is 12% and the estimated beta for Google is 1.23, then what is the expected return of Google per CAMP model. The risk-free rate is 5% Expected return = 5% + 1.23 * (12% - 5%) = 13.61% According to the CAPM, what is the market risk premium given an expected return on a security of 19.6%, a stock beta of 1.2, and a risk-free interest rate of 10%? 19.6% = 10% + 1.2 × (MRP); MRP = 8.00% A pension fund manager is considering three mutual funds. The first is stock fund A, the second is another stock fund B, and the third is a T-bill money market fund that yields a sure rate of 5%. The correlation between the fund returns is 0. Suppose now that your complete portfolio must yield an expected return of 9% and be efficient, that is, on the best feasible CAL. The optimal risky portfolio proportion for stock B is 70% of the risky optimal portfolio. The probability distributions of the risky funds are: (Fund A: (ER) = 10%; (SD) = 15%) (Fund B: (ER) = 20%; (SD) = 25%) Find the expected return of optimal risky portfolio and standard deviation of the whole portfolio: Standard Deviation: ( (70% * 25% )^2 + (30% * 15%)^2 ) = 18% Expected return of risky portfolio: 30%*10%+20%*70% =17% Y of the risky portfolio: 9% = Y * 17% + (1-Y) * 5% Y = 33% Standard deviation of the whole portfolio: 33% * 18% = 6% . Geometric average return offers the most accurate reflection of the true historical performance for an investment, considering reinvestment of dividends and interest. Dollar-weighted return is best suited for assessing specific portfolio’s performance ? . How is the S&P 500 Index and the Dow Jones constructed? Market capitalization-weighted average of 500 large-cap stocks; Price-weighted average of 30 large industrial stocks . . Short sale of a stock : Max potential gain is limited to initial investment; max potential loss is unlimited. . Security on margin: Max potential gain is unlimited , max potential loss is limited to initial investment. . Kurtosis refers to the number of extreme returns in a distribution in the context of investment returns . Standard Deviation measures the risk or volatility of an investment when applied to investment returns . Adding additional risky assets to the investment opportunity set will generally move the efficient frontier up and to the left. . Degree of risk aversion will determine their optimal mix of the risk-free asset and risky asset . How can we determine the optimal risky portfolio among investment choices: By locating the point where the capital market line intersects with the efficient frontier. By tracing the line with the most pronounced incline that connects the risk-free rate to the efficient frontier . The most representative example of systematic risk is a nationwide economic recession leads to a decline in consumer spending and affects multiple industries . If enough investors decide to purchase stocks , they are likely to drive up stock prices , thereby causing expected return to fall and risk premiums to fall . . As you extend the time horizon of your investment and choose to invest over multiple years, you can expect: The average risk per year may decrease over longer investment horizons. The overall risk of your investment will accumulate and increase over time. . To construct a riskless portfolio using two risky stocks , one would need to find two stocks with a correlation coefficient of -1.0 . In a well-diversified portfolio , unsystematic risk is negligible . According to the capital asset pricing model , a security with a positive alpha is considered underpriced plot above the SML . According to the CAPM , investors are compensated for all except the degree of diversification . . Proponents of the EMH think technical analysts are wasting their clients’ time . In a market that is semi-strong form efficient : Stock prices incorporate all publicly available information, such as news reports and financial statements . Most people would readily agree that the stock market is not strong-form efficient . Stocks that exhibit stability over time suggest that the market has not yet factored in new information . Which is not a method employed by fundamental analysts : Relative strength analysis . According to EMH , what investment approach is implied to investors: A passive investment approach, such as index investing or ETFs . What are some key characteristics of market efficiency : There are no arbitrage opportunities . Which of the following would violate the efficient market hypothesis: Investors earn abnormal returns months after a firm announces surprise earnings . In behavioral finance, the concept of "loss aversion" refers to: The tendency of investors to be more concerned about losses than equivalent . The behavioral finance concept of "overconfidence bias" suggests that individuals: Overestimate their knowledge and abilities, leading to suboptimal investment choices . Following a period of falling prices , the moving average will be above the current price . Conventional finance theory assumes investors are rational and behavioral finance assumes some systematic irrationality . In prospect theory within behavioral finance, the concept of "diminishing marginal utility" suggests that: The utility of gains increases at a decreasing rate . When the market breaks through the moving average line from below, a technical analyst would probably suggest that it is a good time to buy the stock . "Relative strength," means that in the recent past a stock has outperformed the market index . In a simple CAPM world : Investors choose to hold the market portfolio, includes all risky assets. Their complete portfolio will vary depending on their risk aversion. Return per unit of risk will be identical for all individual assets. Market portfolio will be on the efficient frontier, it will be the optimal risky portfolio. A higher Sharpe Ratio indicates higher risk-adjusted returns in a portfolio An investor who prefers safe low-risk bonds will have strong risk aversion in their portfolio choices T-bill earns interest by buying the bill at a discount from the face value to be received at maturity Real assets generate income to economy, financial assets define allocation of income to investors Nominal interest rates account for inflation, while real interest rates do not The risk that can be diversified away is Unsystematic Risk. In capital asset pricing model , the systematic measure of risk is best captured by beta The graph of the relationship between expected return and beta in the CAPM is called the SML The SML is valid for both well-diversified portfolios and individual assets and the o CML is valid for well-diversified portfolios only Choosing stocks by searching for predictable patterns in stock prices is called technical analysis Diversification is most effective when security returns are Negatively Correlated Conventional finance theory assumes investors are rational , and behavioral finance assumes some systematic irrationality Stock A has an expected rate of return of 14% and a beta of 1.3. The market expected rate of return is 9%, and the risk-free rate is 4%. The alpha of the stock is: 0.14 – (0.09 + 1.3 × (0.09−0.04)) = 0.035 = 3.5% Using the CAPM formula, if an expected return on a security is 12.5%, the risk-free interest rate is 4%, and the stock's beta is 1.2, the market return is: 12.5% = 4% + 1.2*(Erm-4%), Erm=11.08% You short-sell 200 shares of Tuckerton Trading Company, now selling for $46 per share. What is your maximum possible gain, ignoring transactions cost? 200 × ($46) − 200 × ($0) = 9,200 A stock quote indicates a stock price of $72 and a dividend yield of 3%. The latest quarterly dividend received by stock investors must have been ______ per share. ($72 × 0.030)/4 = $0.54 A T-bill quote sheet has 90-day T-bill quotes with a 5.32 bid and a 5.26 ask. If the bill has a $10,000 face value, an investor could sell this bill for: $10,000 × [1−((0.0526×90)/360) ]= $9,868.50
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