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Liberty University *

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Economics

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Feb 20, 2024

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Consider the following scenario analysis: ___RateofReturn Scenario Probability Stocks Bonds Recession 0.20 -6% 17% Normal economy 0.50 20% 8% Boom 0.30 29% 6% a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms? b. Calculate the expected rate of return and standard deviation for each investment. c. Which investment would you prefer? Complete this question by entering your answers in the tabs below. Required A Required B Required C Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms? Ils it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms? rYes l vI Explanation: Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations. a. Interest rates tend to fall at the outset of a recession and rise during boom periods. Because bond prices move inversely with interest rates, bonds provide higher returns during recessions when interest rates fall. b. rgiocks = [0.2 x (—6%)] + (0.5 x 20%) + (0.3 x 29%) = 17.5% oonds = (0.2 x 17%) + (0.5 x 8%) + (0.3 x 6%) = 9.2% Variancegoos = [0.2 X (=0.06 - 0.17)%] + [0.5 x (0.20 - 0.17)2] + [0.3 x (0.29 - 0.17)%] = 0.015325 Standard deviation = 0.015325” = 12.38% Variancepy,gs = [0.2 x (0.17 - 0.092)%] + [0.5 x (0.08 - 0.092)%] + [0.3 x (0.06 - 0.092)2] = 0.001596 Standard deviation = 0.001596” = 3.99% c. Stocks have both higher expected return and higher volatility. More risk-averse investors will choose bonds, while those who are less risk-averse might choose stocks.

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