Consider a stock portfolio consisting of two units of S¹ and one unit of S². Calculate the probability of delta losses over one day, if the daily log-returns (X₁, X₂) of the stocks are independent with X₁ N(0.5, 1.1), X₂ ~ N(-0.2, 0.5) and the current stocks value are S= 100, S2 = 50.
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Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
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- Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + .7RM + eARB = −2% + 1.2RM + eBσM = 20%; R-squareA = .20; R-squareB = .12What is the covariance between each stock and the market index?Suppose 0.3 is the correlation of returns between any two stocks in an equal-weighted portfolio containing N stocks. Suppose the volatility of any stock is 25%. Calculate the volatility of a portfolio with · N = 24 stocks · N = 100 stocks · N = infinite stocksThe index model for stocks A and B is estimated from excess return with the following results: RA = -0.01 +0.8RM RB = 0.04 + 1.1RM R-squared 4 = 0.15 R-squared B = 0.3 Market-index risk (oM) is 0.2
- Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + .7RM + eARB = −2% + 1.2RM + eBσM = 20%; R-squareA = .20; R-squareB = .12What is the standard deviation of each stock?The index model has been estimated for stock A with the following results: RA = 0.01 + 1.2RM + eA. σM = 0.15; σ(eA) = 0.10. The standard deviation of the return for stock A isSuppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 0.03 + 0.7 RM + eA RB = -0.02+ 1.2 RM + eB σM =0.20; R-square A = 0.25 R-square B = 0.20 What is the standard deviation of A & B, respectively? Group of answer choices 0.54, 0.28 0.28, 0.54 0.45, 0.50 0.50, 0.45
- Assume you have invested in two other stocks: Stock A has a beta of 1.20 and Stock B has a beta of 0.8. Rf= 2% and Rm = 12%. Using CAPM, what are the expected returns for each stock? Return of stock = Risk free rate + beta ( market rate of return - risk free rate of return) Return of Stock A = 2% + 1.20 (12% - 2%) = 2.12% Return of Stock B = 2% + 0.80 (12% - 2%) = 2.08% What is the expected return of an equally weighted portfolio of these two stocks? Weight of stock A = 0.50 Weight of Stock B = 0.50 Expected return = (Return of Stock A * weight of Stock A) + (Return of Stock B * weight of stock B) = (2.12 * 0.50) + (2.08*0.50) = 1.06 + 1.04 = 3% What is the beta of an equally weighted portfolio of these two stocks? Beta of portfolio = (Beta of Stock A * weight of stock A) + (Beta of Stock B * weight of Stock B) = (1.20*0.50) + (0.80*0.50) = 0.60 + 0.40 = 1 Beta of portfolio = 1 (iv) Sketch the SML to represent the…The index model has been estimated using historical excess return data for stocks A, B, and C, with the following results: RA = 0.02 + 0.9RM + eA RB = 0.04 + 1.2RM + eB RC = 0.10 + 1.ORM + eC OM oM = 0.22 o(eA) = 0.21 o(eB ) = 0.11 o(eC ) = 0.23 a. What are the standard deviations of stocks A, B, and C? b. Break down the variances of stocks A, B, and C into their systematic and firm-specific components. c. What is the covariance between the returns on each pair of stocks? d. What is the covariance between each stock and the market index?You have estimated the following probability distributions of expected future returns for Stocks X and Y: Stock X Stock Y Probability Return Probability Return 0.1 -12 % 0.2 4 % 0.1 11 0.2 7 0.3 14 0.3 11 0.3 30 0.2 17 0.2 40 0.1 30 What is the expected rate of return for Stock X? Stock Y? Round your answers to one decimal place.Stock X: % Stock Y: % What is the standard deviation of expected returns for Stock X? For Stock Y? Round your answers to two decimal places.Stock X: % Stock Y: % Which stock would you consider to be riskier? is riskier because it has a standard deviation of returns.
- The index model for stock A has been estimated with the following result: RA = 0.01 + 0.9RM + eA. If σM = 0.25 and R2A = 0.25, the standard deviation of return of stock A is:1. Consider 3 stocks A, B, and C and the risk-free rate RF=0.5%. The logarithmic rates of return are as follows: 1 4 8. RA1(%) RB,(%) Rc.(%) -2 2 7 9 3. 7 4. 8. 3. -1 -5 a) Compute the mean returns the holding returns for the entire period. b) Determine the risk of each stock. c) Measure the correlation between A and B, A and C, and B and C. d) Compute the expected return and risk for the following portfolios: •P1:40% from the budget was invested in A and the rest of the money in B • P2: XA-40%, xc=60% • P3: XA-30%, Xg=30%, xC-40% P4: Xp3-70%, xRF=30%Assume that using the Security Market Line(SML) the required rate of return(RA)on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourthof the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A(A) to beta of B(B).