Question

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4. What is the expected return on an IBM bond if the return is 3% one fifth of the time, 10% two fifths of the time, 12% one fifth of the time, and 8% the rest of the time? Rexpected - E Priori Variance ? Probabilitystate (Returnstatei - Rexpected) Standard Deviation = =yo a. Estimate the Variance and Standard Deviation (Just fill in the table below). REP R -Rexpected (R-Remete) (R- TOTAL: VARIANCE STANDARD DEVIATION b. Determine the ranges of your return with 68,95 and 99 percent probability. Show your work in a normal distribution chart. Normal Distribution c. Is this a risky asset? Why?

Answer 1

all r 4.a. Let X : return on bond, It is given, X = 3; with probty = 1/5; X = 10; with probty = 2/5; X = 12; with probty = 1/5; X = 8; with probty = 1/5; E(X)= * Pr(X = 1) = 43/5 = 8.6 Var(X) = E(X2) – E(X)?: E(X) = 2?P(X = 1) = 83.4; all r So Var(X) = 83.4 - (8.6%) = 9.44 , Std.dev = 9.44 = 3.07 b. We know from empirical rule : 68%range = (E(X) - 0, E(X) +0) = (5.53, 11.67); 95%range = (E(X) – 20, E(X) +20) = (2.46, 14.74); 99%range = (E(X) – 30, E(X) +30) = (-0.61, 17.81); c. Yes, this is risky asset class because std.dev is very high and each of the ranges in part b, is also wildly fluctuating.

Table is filled below :

Ri	Pri	Ri-Rexp	(Ri-Rexp)^2	(Ri-Rexp)^2 * Pri
3	1/5	-5.6	31.36	6.272
10	2/5	1.4	1.96	0.784
12	1/5	3.4	11.56	2.312
8	1/5	-0.6	0.36	0.072
			Var	9.44
			stddev	3.07

Normal plot is shown below :

- + + . 68) 95) -6, 6) 244 5.53 8. 1, 6% 16.14 (18)