Question

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There are three securities in the market. The following chart shows their possible payoffs: State Return on Return on Return on Outcome me Security 1 Security 2 Security 3 191 041 34 141 .091 .091 091 .141 .141 16 .041041191 -16 .191 NM .34 a-1. What is the expected return of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Security 1 Security 2 Security 3

Answer 1

average For a security Expected return is the weighted verage of all possible returns Weights here are the probabilities For security I E(M) - (0.16 x 0:191) + [o 34 x0.4+1) +(6:34 x 0.091)+ (0-161004) = 0.03056 +0.04794 +0 0309+ +0.00656 0.116 = 11. 60% Similarly, for security 2 E -C0-1680191) + (0-3470.091] + [034 x0.141) + 00+1) for semnity 16 - 1160% ECH). (016-04) + (034x0.00] +0.34 20 147) + (Otev :197) = 0.116 11.60% (A-2) Standard deviation o- Je (2; -21) Pi u is the expected return x, is the ith return Pi is the probability of ith return state x ul (2; -7 1² for e for security severity 1 1 (0.116-0:16 = +0.075 0.005625 2 (0.116 - 0.141) = +0.025 0.000695 (0.116 0.091)=-0.025 0.000625 4 (0.116-0.016) = 0.075 0.005 625 o por seurity 1 = 0.0056 2 5 x 0.16 + 0.000625 70 32 +0.000 625xo 34 to 0.005625xo.16 0.04717 = 4.72%

for state semarity 2 seurity for &late 4 -0.075 - ai -0.075 0.075 -0.025 0.025 0.025 to 025 0.075 we can see that since a-x, of the 2 securities are same in value o order as that of Sewerty 1 o of security a= o of security 3 -o of security 1 = 4.72%. variance = { Pix(x; -1) (y; -7.) 3 Let us call security 1 as x a as y and 3 anz state xin y- ý zi-2 | Pi T +0.075 0.075 -0.075 +0.025 1 -0.025 0.025 3 -0.025 0.025 0.025 4 - 0.075 20.075 0.075 0.16 0.34 0.34 0.16 Covarianue (1,2)= 0.075 x 0.075 0.16 + 0.025 (-0.025) X034 + 6o 025 x0 025) x 0.34 + (-0-075 x -0.015) + 0.16 0.0013 75

Covariance (2, 3) (0.075 x -0.015) *0.16 + (-0.025 x(-0·025) 20:34 + ( o 025 xo oa 5)70-34 +(-0.075 x 0.075) xo.16 = -0.001375 covariance (1,3) = (0.0758 -0.075) x0 16 + (0.025 -0.025) 80.34 +(-0.025 x0025 x0.34 + (-0.075X0-075) x0.16 -0.00 22 25 (62) Correlation = covariance (1,2) 0.001375 C1,2) (0.04717² = 0.617 978 correlation Covariance (2,3) -0.001375 = 02x03 (0.04717) -=0.61797 correlation - covariance (1,3) 0908 (1,3) -0.002225 (0.4717)

Elm of security 1 = 11.6% ECA of security a = 11.6% E (n) of we invest in 1 $ 2 mi 50% each = 0.5x11.6% to 5*11.6%