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Expected Value --> to Variance --> to Standard Deviation

Topic: Decision Alternatives Suppose that the percentage annual return you obtain when you Invest a dollar In gold or the stock market ls dependent on the general state of the national economy as Indicated below. For example, the probability that the economy will be In "boom" state ls {1.15. In this case, If you Invest In the stock market your return ls assumed to be 25%; on the other hand If you Invest In gold when the economy Is In a "boom" state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1--and ls. State of economy Gold Return 4%} m {-14%} Find the expected value, variance and standard deviation via the information provided. Given your ndings, which invmtment would be riskier and why? 5E 11!: EIEcted 1Value la -m - 13.6 {Married Galdreturn -I3.Iiil We've already completed the first step [aheve] cf the prchleln by finding the Expected 1ufalue {aka Mean] cfh-cth the market [3.5) and geld (13.6}. Next we need ta nd the 't-hriance efhcth as fellcwa uah1g the fennula: Vali} - Ealp - u? {Methad} Tc calculate the 1i..l"ariance: I aquare each value and multiply by its pmhahility I aumthemupandwe get Ell]: I then subtract the square cf the Expected 1Value 11.1 Se all we eaaentialljr have tc do is square the iufcrmaticn in the tables ahcve cf {IF} and then subtract the sum from the square cf cur expected 1valuehuean fer the variance (Step 1). 1 : Variance MARKET rm-(X) - 212;: p2} {Market Variance - 5.25} VariX} 12:2]; - p2 -1'T - 3.5\": - 65.25 {Gold Variance - 45?. F6] vans} 22:31.5 - .112 = 25.2 115:5: = 451.55 Lastly, to find the standard deviation we simply take the square rant af'eaeh ef the 1ir'hriantvas aheve Fermdla: n = WariX] St El- : Standard Deviation NET: a = Warts} = $55.25 = 5.43 = {5145 Market standard Deviation] GnLnr a = Warq = 115175 = 12.5503 = ($12.55 edld Standard Deviatien] *** Therefere, in can he said that altheugh geld has a higher expected return versus the market {116% vs. 8.5%}, it is a far riskier investment due tn its higher standard deviatien {$11.55 versus $145]