Search this course X Consider the following two probability distributions of expected future returns for stocks A and B: Return Stock A Stock B Probability (%) (%) 0.1 1% -3.5% 0.2 0.2 0.4 1.2 2 0.2 2 2.5 0.1 3.8 4.5 N Suppose you know that the expected rate of return for stock A is 1.2% and would like to calculate the expected return for stock B. For each row in the table, indicate the approximate value of product of the rate of return for stock B multiplied by the probability of that return. Return Pi XTi Stock B () Probability (% ) 0.1 -3.5% 0/ 0.2 O 0.4 2 0.2 2.5 0.1 4.5 Using your answers from the nQ - RISK and Rates of Return 0.2 0.2 0 0.4 1. 2 2 0.2 2 2.5 0.1 3.8 4.5 Suppose you know that the expected rate of return for stock A is 1.2% and would like to calculate the expected return for stock B. For each row in the table, indicate the approximate value of product of the rate of return for stock B multiplied by the probability of that return. Return Pi Xri Stock B (%) Probability (%) 0.1 -3.5% 0.2 O 0.4 2 0.2 2.5 0.1 4.5 Using your answers from the previous part of the question, the expected rate of return for stock B is approximately %. 5.5 Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate andard deviation of expected returns for stock A. 1.4 Hint: Recall that the expected rate of return for stock A is 1.2%. 0.85mapsh... Q Searc video Lesson - Risk and Rates of Return Definition Expected Rate of Required Rate of Return Realized Rate of Return Return A rate of return calculated based on the likelihood of various possible returns. O O O A rate of return needed by investors to compensate for the risk of an investment. O O O The actual return received from an investment. O O O Read the following passage of text and answer the questions that follow. There are a few fundamental concepts when first learning to assess and analyze an investment's risks - both in isolation and as part of a portfolio. One such concept is that of a probability distribution, which outlines possible outcomes along with the probability of that outcome occurring. Using such a distribution, you can then estimate a probability-weighted average known as an expected value. In the context of an investment, this could be used to calculate an expected rate of return for an investment, or a probability-weighted average return, based on the probability of various returns being realized. While the expected returns from an investment is useful, it does not tell the whole story with regards to the risk of that investment. While there are many definitions of risk, one simple measure of stand-alone risk can be calculated from the probability distribution of the investment returns. For example, you can use the standard deviation to measure how tight, or how spread out, the probability distribution is around the expected value. An investment with a high standard deviation of expected returns will have a probability distribution that is more spread out, implying that the probability of the realized return being different than the expected (probability-weighted) return is higher. Conversely, when the standard deviation is low, the probability of the realized return of the investment being much different than the expected return is low. In the next stage of this problem, you will learn how to calculate both the expected return and standard deviation of expected returns for a pair of investments. True or False: The standard deviation of expected returns of a stock is one measure of the standalone risk of a stock.Return \\ Stock A Stock B Probability (%) (\"/0) ~0.1\\ '2-5% -8,75% 0.2 0.5 o 0.4 3 5 0.2 5 6.25 01 9.5 11.25 Suppose you know that the expected rate of return for stock A is 3% and would like to calculate the expected return for stock B. The expected rate of return for stock B is approximately :- %. Suppose you know that the standard deviation of expect expected returns for stock A. Hint: Recall that the expected rate of return for stock A i The variance of the expected returns for stock A is appro while the standard deviation of expected returns for stock A is ' approximately V /o. Using your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximately . . . - u " True or False: Investors will always View the stock With a lower coefment of variation as a safer c home when compared to a stock with a higher coefficient of variation. Q Search this cou insider the following two probability distributions of expected future returns for stocks A and B: Return Stock A Stock B Probability (%) (%) 0. 1 -2.5% -8.75% 0.2 0.5 O 0.4 3 5 0.2 5 6.25 0.1 9.5 11.25 Suppose you know that the expected rate of return for stock A is 3% and would like to calculate the expected return for stock B. The expected rate of return for stock B is approximately % . Suppose you know that the standard deviation of expected returns for stock B is 5.0867% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 3%. The variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately %. 9 .3 Using your calculations in the previous parts of the problem, the co 82.75 f variation of stock B is approximately 26.875 True or False: Investors will always view the stock with a lower coel variation as a "safer" choice when compared to a stock with a higher coefficient of variation. 0.050.4 3 5 0.2 5 6.25 0. 1 9.5 11.25 Suppose you know that the expected rate of return for stock A is 3% and would like to calculate the expected return for stock B. The expected rate of return for stock B is approximately % . Suppose you know that the standard deviation of expected returns for stock B is 5.0867% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 3%. The variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately % . Using your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximately 8.5867 True or False: Investors will always view the stock with a lower coefficient of variation as a "safer" choice when com stock with a higher coefficient of variation. 1.5867 O True 17.8036 1.4534 O FalseVI TULUITT TVP SEVEN D TO UPPIVATTIVITY Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - r)2 0.1 -1% 0.2 0.2 0.4 1.2 0.2 2 0.1 3.8 Using your answers from the p 2.5 part of the question, the variance of the expected returns for stock A is approximately while the standard deviation of expel 6.76 urns for stock A is approximately % 0.26 Let o represent the standard of a stock's returns and r represent the expected returns of that stock. 0.676 The formula for calculating the coefficient of variation for a stock's return is . Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximatelySearch Return Stock A Stock B Probability (%) (%) 0.1 -1% -3.5% 0.2 0.2 0 0.4 1.2 2 0.2 2 2.5 0. 1 3.8 4.5 Suppose you know that the expected rate of return for stock A is 1.2% and would like to calculate the expected return for stock B. For each row in the table, indicate the approximate value of product of the rate of return for stock B multiplied by the probability of that return. Return Pi X Ti Stock B (%) Probability (% ) 0.1 3.5% 0.2 0.4 2 0.2 2.5 0.1 4.5 0.25 Using your answers from the 2.5 part of the question, the expected rate of return for stock B is approximately %. 0.5 Suppose you know that the sta leviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. 0.210 . Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - r ) 2 0.1 -1% 0.2 0.2 0.4 1.2 1 0.2 2 0.1 3.8 0.196 -0.1 Using your answers from the p part of the question, the variance of the expected returns for stock A is approximately while the standard deviation of expel 0.2 urns for stock A is approximately %. Let o represent the standard deviation of a stock's returns and r represent the expected returns of that stock. The formula for calculating the coefficient of variation for a stock's return is .Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximatelyReturn Stock A Stock B Probability (%) (%) 0.1 -1% -3.5% 0.2 0.2 0 0.4 1.2 2 0.2 2 2.5 0. 1 3.8 4.5 Suppose you know that the expected rate of return for stock A is 1.2% and would like to calculate the expected return for stock B. For each row in the table, indicate the approximate value of product of the rate of return for stock B multiplied by the probability of that return. Return Pi Xri Stock B (%) Probability (%) 0.1 3.5% 0.2 0.4 N 0.2 0.2 2.5 0. 1 4.5 0 Using your answers from the previous part of the question, the expected rate of return for stock B is approximately %. Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A.Q Se Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - 7) 2 0.1 -1% 0.2 0.2 0.4 1.2 0.2 2 0.1 3.8 Using your answers from the previous part of the question, the variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately %. Let o represent the standard deviation of a stock's returns and r represent the expected returns of that stock. The formula for calculating the coefficient of variation for a stock's return is _m. Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximatelySuppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - 7) 2 0.1 1% 0.2 0.2 0.4 1.2 0.2 2 0.1 3.8 Using your answers from the previous part of the question, the variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately %. Let o represent the standard deviation of a stock's returns and r represe 0.1414 bected returns of that stock. 2.0736 The formula for calculating the coefficient of variation for a stock's return Using this formula, along with your calculations in the previous 1.2198 parts of the problem, the coefficient of variation of stock B is approximat 3.6387 Step 3: Practice: Expected ReturnsSearch t 10 . Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - r)2 0.1 -1% 0.2 0.2 0.484 0.4 1.2 0.2 2 0.004 0.1 3.8 -0.22 Using your answers from the 4.84 part of the question, the variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately %. Let o represent the standard deviation of a stock's returns and r represent the expected returns of that stock. The formula for calculating the coefficient of variation for a stock's return is _.Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximatelyQ Search this course X 10 . Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - 7 ) 2 0.1 -1% 0.2 0.2 0.4 1.2 0.2 2 0.1 3.8 Using your answers from the previous part of the question, the variance of the expected returns for stock A is approximately V while the standard deviation of expected returns for stock A is approximately %. Let o represent the standard deviation of a stock's returns and r represent the expected returns of that stock. A+ The formula for calculating the coefficient of variation for a stock's return is _. Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximatelySearch this co Consider the following two probability distributions of expected future returns for stocks A and B: Return Stock A Stock B Probability (%) (%) 0.1 -2.5% -8.75% 0.2 0.5 0.4 3 5 0.2 5 6.25 0.1 9.5 11.25 Suppose you know that the expected rate of return for stock A is 3% and would like to calculate the expected return for stock B. The expected rate of return for stock B is approximately %. Suppose you know that the standard deviation of expected returns for stock B is 5.0867% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 3%. The variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately Using your calc 5.1841 the previous parts of the problem, the coefficient of variation of stock B is approximately 9.0967 True or False: I ill always view the stock with a lower coefficient of variation as a "safer" choice when compared to a stock with a higher 0.2236 coefficient of va 3.0496VI TULUITT TVP SEVEN D TO UPPROAIMTIVITY Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - r)2 0.1 1% 0.2 0.2 0.4 1.2 0.2 2 0. 1 3.8 0.64 Using your answers from the p 1.024 part of the question, the variance of the expected returns for stock A is approximately while the standard deviation of expel urns for stock A is approximately %. 0.08 Let o represent the standard c 0.128 of a stock's returns and r represent the expected returns of that stock. The formula for calculating the coefficient of variation for a stock's return is _.Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximatelyQ s Lesson - Risk and Rates of Return Return Stock A Stock B Probability (%) (% 0.1 -1% 3.5% 0.2 0.2 O 0.4 1.2 2 0.2 2 2.5 0.1 3.8 4.5 Suppose you know that the expected rate of return for stock A is 1.2% and would like to calculate the expected return for stock B. For each row in the table, indicate the approximate value of product of the rate of return for stock B multiplied by the probability of that return. Return Pi X Ti Stock B (%) Probability (%) 0.1 -3.5% 0.2 O -0.35 0.4 N 0.2 2.5 0.1 0.1 1.5 -0.7 Using your answers from the -3.5 part of the question, the expected rate of return for stock B is approximately _ %. Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A.Q Search Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability % pix (ri - 7 ) 2 0.1 -1% 0.2 0.2 0.4 1.2 0.2 2 0. 1 3.8 Using your answers from the previous part of the question, the variance of the expected returns for stock A is approximately V while the standard deviation of expected returns for stock A is approximately %. Let o represent the standard deviation of a stock's returns and r represent the expected returns of that stock. The formula for calculating the coefficient of variation for a stock's return is . Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximately Step 3: Practice: Expected Returns 3.4347 0.634699 Now it's time for you to practice what you've learned. 2.8486 Consider the following two probability distributions of expected future returns and B: 1.4534Return Stock A Stock B Probability (%) (%) 0.1 -1% -3.5% 0.2 0.2 0 0.4 1.2 2 0.2 2 2.5 0.1 3.8 4.5 Suppose you know that the expected rate of return for stock A is 1.2% and would like to calculate the expected return for stock B. For each row in the table, indicate the approximate value of product of the rate of return for stock B multiplied by the probability of that return. Return Pi X Ti Stock B (%) Probability (%) 0.1 -3.5% 0.2 0 0.4 2 0.2 2.5 2 0.1 4.5 0.4 Using your answers from the part of the question, the expected rate of return for stock B is approximately 0.8 Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A.Q se 0.2 0.2 0 0.4 1.2 2 0.2 2 2.5 0. 1 3.8 4.5 Suppose you know that the expected rate of return for stock A is 1.2% and would like to calculate the expected return for stock B. For each row in the table, indicate the approximate value of product of the rate of return for stock B multiplied by the probability of that return. Return Pi X Ti Stock B (%) Probability (%) 0.1 -3.5% % 0.2 0.4 2 0.2 2.5 0.1 4.5 4.5 Using your answers from the p part of the question, the expected rate of return for stock B is approximately %. 0.1 Suppose you know that the sta eviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of 0.9 expected returns for stock A. 0.45 Hint: Recall that the expected return for stock A is 1.2%.Sea Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - 7) 2 0. 1 -1% 0.2 0.2 0.4 1.2 0.2 2 0.1 3.8 Using your answers from the previous part of the question, the variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately %. 0.02 Let o represent the standard deviation of a stock's returns and r represent the expected returns of that stock. 4.3 1.488 The formula for calculating the coefficient of variation for a stock's return is Using this formula, along with your calcula the previous parts of the problem, the coefficient of variation of stock B is approximately 13.24 Step 3: Practice: Expected ReturnsQ s A rate of return needed by investors to compensate for the risk of an investment. O O The actual return received from an investment. O O O Read the following passage of text and answer the questions that follow. There are a few fundamental concepts when first learning to assess and analyze an investment's risks - both in isolation and as part of a portfolio. One such concept is that of a probability distribution, which outlines possible outcomes along with the probability of that outcome occurring. Using such a distribution, you can then estimate a probability-weighted average known as an expected value. In the context of an investment, this could be used to calculate an expected rate of return for an investment, or a probability-weighted average return, based on the probability of various returns being realized. While the expected returns from an investment is useful, it does not tell the whole story with regards to the risk of that investment. While there are many definitions of risk, one simple measure of stand-alone risk can be calculated from the probability distribution of the investment returns. For example, you can use the standard deviation to measure how tight, or how spread out, the probability distribution is around the expected value. An investment with a high standard deviation of expected returns will have a probability distribution that is more spread out, implying that the probability of the realized return being different than the expected (probability-weighted) return is higher. Conversely, when the standard deviation is low, the probability of the realized return of the investment being much different than the expected return is low. In the next stage of this problem, you will learn how to calculate both the expected return and standard deviation of expected returns for a pair of investments. True or False: The standard deviation of expected returns of a stock is one measure of the standalone risk of a stock. O True O FalseConsider the following two probability distributions of expected future returns for stocks A and B: Return Stock A Stock B Probability (%) (%) 0.1 -2.5% -8.75% 0.2 0.5 0.4 3 5 0.2 5 6.25 0.1 9.5 11.25 Suppose you know that the expected rate of return for stock A is 3% and would like to calculate the expected return for stock B. The expected rate of return for stock B is approximately %. Suppose you know that the standard deviation of expected returns for stock B is 5.0867% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 3%. The variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately % . Using your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximately True or False: Investors will always view the stock with a lower coefficient of variation as a "safer" choice when compared to a stock with a higher coefficient of variation.Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A. Hint: Recall that the expected rate of return for stock A is 1.2%. For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A. Return Stock A Probability (%) pi X (ri - r ) 2 0.1 -1% 0.2 0.2 0.4 1.2 0.2 2 0 0.1 3.8 0.576 Using your answers from the previous part of the question, the variance of the expected returns for stock A is approximately while the standard deviation of expected returns for stock A is approximately %. Let o represent the standard deviation of a stock's returns and r represent the expected returns of that stock. The formula for calculating the coefficient of variation for a stock's return is _. Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximately