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Final_2006_solutions

# Final_2006_solutions - 9456 e 025 105-100 = 5 3531(b Delta...

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ORIE 473 — Final Exam Solutions Professor David Ruppert 1. (a) gross return = 250/230 = 1.0870 net return = net return - 1 = 0.0870 (b) (100 * 250 + 200 * 15) / (100 * 230 + 200 * 12) - 1 = 0 . 1024 2. (a) e 3 (b) e 3+Φ - 1 (0 . 2) 3. γ (0) = 1 . 1 2 + . 2 2 + ( - . 3) 2 = 1 . 14 γ (1) = . 1 + . 1 * . 2 + . 2 * ( - . 3) = . 06 Similarly, γ (2) = . 17 and γ (3) = - . 3. Thus, ρ (1) = . 06 / 1 . 14 = . 0526 and similarly ρ (2) = . 17 / 1 . 14 and ρ (3) = - . 3 / 1 . 14. Of course, ρ (0) = 1. 4. The interpretation is that the last two explanatory variables are highly correlated with each other. The first three explanatory variables are not highly correlated with each other or with the last two variables. The best fitting model might use only one of the last two variables. 5. (a) beta = . 5 * 1 . 7 + . 2 * 1 . 1 + . 3 * . 5 = 1.22 (b) var excess return = . 5 2 * . 018 + . 2 2 * . 012 + . 3 2 * . 01 = 0.0059 (c) (beta 2 * . 015) / (beta 2 * . 015+var excess return) = 0.7915 6. (a) ( 2 . 2 ) . 1 2 . 1 * 3 * . 35 . 1 * 3 * . 35 3 2 2 . 2 + . 1 2 = . 4940 (b) ( 2 . 2 ) . 1 2 . 1 * 3 * . 35 . 1 * 3 * . 35 3 2 3 . 4 = . 9270 7.
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Unformatted text preview: . 9456 + e-. 025 105-100 = 5 . 3531 (b) Delta of put = Delta of call-1 = 0 . 4255-1 =-. 5745 (c) Vega of put = Vega of call = 39.1 8. (a) W 3 + 4 (b) 14 (c) 6 (d) expected value = 0 variance = 8 9.-10 , 000 * { . 1 + . 2Φ-1 ( . 05) } = 2 , 289 . 7 10. (a) E ( Y t | X t = 2 , a t-1 =-1 and σ t-1 = 0 . 5) = . 5 + . 3 * 2 + . 4 * √ 1 + . 2 = 1 . 5382 (b) 1.2 (c) It is normal. If one conditions on X t and a t-1 , then Y t is a ﬁxed constant (speciﬁcally, β + β 1 X t + δσ t ) plus ² t times another ﬁxed constant σ t-1 . Therefore, since ² t is normally distributed, Y t is conditionally normally distributed. (d) No it is not normal, but rather a normal mixture...
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