FIN410 - Exam 1

The correlation coefficient is bounded by what two numbers? ___ and ___.

-1 and 1

Discuss the 3 difficulties with measuring beta that we discussed.

1. It measures the past, not the future. There are a variety of reasons why past performance is considered an unreliable indicator of future results. 2. It measures fluctuations, not loss. 3. It ignores price and it is relative to an unreliable standard.

Name two alternative models to the CAPM.

1. The Market Model. The market model says that the return on a security depends on the return on the market portfolio and the extent of the security's responsiveness as measured by beta. In CAPM also return of security depends on market return and its beta. Therefore it can be consider as alternative of CAPM. 2. Arbitrage Pricing Theory (APT). a multi-factor asset pricing model based on the idea that an asset's returns can be predicted using the linear relationship between the asset's expected return and a number of macroeconomic variables that capture systematic risk.

Define a perpetuity.

It is an annuity that is going to continue forever because these are streams of cash flows that will be payable or receivable till infinity and they do not have a time limit.

What does it mean if a portfolio is efficient?

also known as an "optimal portfolio", is one that provides the best expected return on a given level or risk, or alternatively, the minimum risk for a given expected return.

The slope of the security market line is __________________ and the slope of a stock's characteristic line is ________________.

Beta, since the slope of the of security line gives the market risk premium, security market line. the excess return of market per unit risk.

You have recently been looking over 3 stocks to consider purchasing that might be "good" values and you have calculated the expected returns. The current risk free rate is 3%, and you estimate the market risk premium is 6%. a. What is the equation of the security market line (SML) and what are the required returns for each stock? Which tock would be the best value? Security Expected Return Beta ABC Inc. 9.0% 1.0 Hops Beer Inc. 10.9% 1.2 Tech Inc. 12.1% 1.5 b. Suppose you made a portfolio of the 3 stocks above and invested $5,000 in ABC, $10,000 in Hops Beer, and $5,000 in Tech. Inc. What is the beta of the portfolio, and the fund's required rate of return?

A. Equation of the SML SML is required return = risk-free rate of return + beta (market return - risk-free rate of return) or Ri = Rf + Bi (Rmf) Security Required Return formula Required Return ABC Inc 3% + 1.0*(6%) 9% Hops beer Inc. 3% + 1.2*(6%) 10.2% Tech Inc. 3% + 1.5*(6%) 12% Analysis - Security Hops beer and tech inc are undervalued since its expected return are greater than return required. Security of ABC Inc is at equilibrium i.e. neither undervalued or overvalued. Hence one should invest in either Hops beer Inc. or Tech Inc. since required return is less than expected return. Both securities are better than ABC Inc Hops beer Inc generate less return and Tech Inc generate more return but both have different beta value. Hops beer is less volatile/Risky and Tech Inc is more volatile/Risky. Hence Hops beer Inc carry less return and less risk but Tech Inc. carry more return and more risk. b. Portfolio Beta Portfolio Beta = W1*B1 + W2*B2 + W3*B3 W = Weight B = Beta Total invested amount = ($5000+$10000+$5000) = $20000 ABC Inc. Weight (5000/20000) = 0.25 beta = 1.0 portfolio beta = 0.25 Hops Beer Inc Weight (10000/20000) = 0.5 Beta = 1.2 Portfolio Beta = 0.6 Tech Inc. Weight (5000/20000) = 0.25 Beta = 1.5 Portfolio Beta = 0.375 Total Portfolio Beta (0.25+0.6+0.375) = 1.225 Funds Expected Return Funds Expected Return = W1*R1 + W2*R2 + W3*R3 ABC Inc. Weight 0.25 Expected Return 9% Funds Expected Return (0.25*9%) = 2.25% Hops Beer Inc. Weight 0.5 Expected Return 10.9% Funds Expected Return 5.45% Tech Inc. Weight 0.25 Expected Return 12.1% Funds Expected Return 3.0255%

You have owned the following two stocks over the past 5 years. Year Stock A's Price ($) Stock B's Price ($) 2014 67 31 2013 46 25 2012 44 23 2011 50 18 2010 34 19 What is the standard deviation of a portfolio's return in which 50% of your portfolio is in each stock? (Hint, calculate the holding period returns first).

Calculate the holding period returns for Stock A and Stock B. Year Stock A (HPR) 2014 67/46-1 = 45.65% 2013 46/44-1 = 4.55% 2012 44/50-1 = -12.00% 2011 50/34-1 = 47.06% 2010 34 Year Stock B (HPR) 2014 31/25-1 = 24% 2013 25/23-1 = 8.7% 2012 23/18-1 = 27.78% 2011 18/19-1 = -5.26% 2010 19 Formula used for calculation of standard deviation of portfolio: Formula = w12σ12 + w22σ22 + 2w1w2Cov1,2 w1 = the portfolio weight of the first asset w2 = the portfolio weight of the second asset σ1= the standard deviation of the first asset σ2 = the standard deviation of the second asset Cov1,2 = the covariance of the two assets, which can thus be expressed as p(1,2)σ1σ2, where p(1,2) is the correlation coefficient between the two assets Where Wa = weight of stock A = 0.5 Wb = weight of stock B = 0.5 Oa = Standard Deviation of Stock A = 29.70% Ob = Standard Deviation of Stock B = 15.15% COVab = Covariance of Stock A & B = -2.08% Conclusion: Standard Deviation of Portfolio of Stock A and B (oab) is = 16.53%.

What is the name of the line which gives all risk - return possibilities for different weights of stock in a portfolio?

Capital Market Line (CML)

Assume a normal probability distribution. Blue River Toys has an expected return of 13% and a standard deviation of 27%. Thus, we can expect there would be a 68.26% probability that their actual return would be in the range of ______ to ______, and a 95.46% probability that their actual return would be in the range of ______ to ______.

Expected return = 13% Standard Deviation = 27% 68.26% probability that their actual return would be.... Range = expected return +/ - 1 (standard deviation) = 13% +/- 1(27%) = 13% - 1(27%) = -14 = 13% + 1(27%) = 40 = [-14%, 40%] and 95.46% probability that their actual return would be... Range = expected return +/- 2 (standard deviation) = 13% +/- 2(27%) = 13% - 2(27%) = -41 = 13% + 2(27%) = 67 [-41%, 67%]

The present value of an annuity increases as n (the number of payments) increases. True or False?

False

You own a portfolio of two stocks. Red River Inc. has an expected return of 9% and a standard deviation of 15% while Boston Harbor Co. has an expected return of 15% with a standard deviation of 19%. A. What percent of your portfolio must you invest in each stock if you wanted to earn a 12.4% return on the portfolio? (Hint: Consider W1+W2=1.0) B. If the correlation coefficient is 0.3, what is the standard deviation of this portfolio? Is risk reduced at these weights relative to the risk of the individual assets? Why?

Given Information: Red River Inc. Expected Return = 9% Standard Deviation = 15% Boston Harbor Co. Expected Return = 15% Standard Deviation = 19% A. Portfolio Expected Return = 12.4% 12.4% = Wa x 9% + Wb x 15% = 1(-Wb) x 9% + 15% Wb = 9% - 9% Wb + 15 Wb 12.4% = 9% + 6 Wb Wb = 3.4%/6 = 56.6% Wa = 43.4% B. Standard Deviation of Portfolio (Op) SD(A) = 15%, SD(B) = 19%, R = 0.3 Portfolio SD = (WA)^2*(SDA)^2+(SBD)^2+2WA*WB*(SDA)*(SDB)*(r) Portfolio SD = SQRT [(0.4333)^2*(15)^2+(0.5667)^2*(19)^2+2^(0.4333)*(0.5667)*(15)(19)(0.3)] = Portfolio SD = 14.1481 The risk of the portfolio is lower than the risk of individual stocks. The reason is low level of correlation between the two stocks.

ABC Tech has a 12.5% expected return, beta = 0.8 and a 27% percent standard deviation. Blue Sky Toys has a 14% expected return, beta equal to 1.3 and a 23% standard deviation. If the risk free rate is 5% and the expected return on the market it 10%, which stock is riskier for a diversified investor? Why?

Given the following information: ABC Tech Expected Return = 12.5% Beta = 0.8 Standard Deviation = 30% Blue Sky Toys Expected Return = 14% Beta = 1.3 Standard Deviation = 23% To understand which stock would be more attractive to investors, we need to find the value of the coefficient of variation. The coefficient of variation is used to determine how much volatility the stock shows in comparison to its return. Formula: Coefficient of Variation = Standard Deviation/Expected Return ABC Tech Coefficient of Variation = 27%/12.5% = 2.16 Blue Sky Toys Coefficient of Variation = 23%/14% = 1.64 The coefficient of variation should be low for diversification because it reduces the risk. Therefore, Blue Sky Toys is more attractive to diversified investors.

The present value of annuity due is __________ (<,>,=) the present value of an ordinary annuity.

Greater (>). Present value of annuity due is greater than the present value of ordinary annuity. It is a result of the time value of money principle, as annuity due payments are received earlier.

Starting with a graph of the efficient frontier in risk-return space, explain how investors who have the ability to borrow or lend at the risk free rate may find an optimal portfolio based on their level of risk aversion. (You should include the market portfolio, capital market line and indifference curves). In addition show how the formula for the capital market line is determined.

Investors would make an optimal allocation between various assets classes based on their risk aversion. An investor who is very risk averse meaning to have a high risk aversion would invest solely in bonds and certificate of deposits. These investments are considered risk free as there is no risk of default and hence the return would be below par. Such individuals will find it hard to beat inflation. As the risk aversion coefficient decreases, the investor have more appetite for risk and invest in risky assets like equity and derivatives and even speculation. The formula for Capital Market Line is determined as: Expected Return on the portfolio E (Rp) = Rf + [E(Rm) - Rf/Sm] *Sp Where Rf is the risk free return E (Rm) is the expected return on the market Sm is the Standard Deviation of the market. Sp is the Standard Deviation of the Portfolio.

Define systematic and unsystematic risk (and which is diversifiable).

Systematic Risk - is a non-diversifiable risk or market risk. Can be thought of as the probability of a loss that is associated with the entire market or a segment. Unsystematic Risk - is diversifiable, meaning (in investing) if you buy shares of different companies across various industries you can reduce this risk.

You are currently considering the purchase of a vacation home in the mountains. You have been pre-qualified for a 15 year fixed rate mortgage at 5.90%. The home costs $375,000 and you plan on making a down payment of 20% and financing the rest. a. What is your monthly payment not including property taxes and insurance? b. Amortize the first two monthly payments Pmt # Interest Principal Remaining balance 1 _________ ________ _______________ 2 _________ ________ _______________

a. PV=-375000*80%=-300000 is loan amount after paying 20% down payment. FV=0 N=15*12=180 month 1/Y=5.90/12=0.491667 Click CPT Click PMT=2515.39 IS ANSWER as monthly payment. b. First month interest = 5.9%/12 x 300,000 = 1,475, First month principal = 2,515.39 - 1,475 = 1,040.39 Outstanding loan = 300,000 - 1,040.39 = 298,959.61 and so on...