5. Suppose we have a risky asset with random return R. We have defined R to be, S₁ - So So R = Now we introduce the log-return, which is defined as R assume that R~ N(μ, o²) where μ = 0 and o² = 0.1. = In (st). In this question, (i) Show that R = eR 1. (ii) Calculate VaR0.95 for an investment of £150. Remember that if X~ N(μ,0²) then exis lognormally distributed with parameters and o2. You may use that for a standard normal random variable -¹(0.05) = -1.6449, where & denotes the CDF.
5. Suppose we have a risky asset with random return R. We have defined R to be, S₁ - So So R = Now we introduce the log-return, which is defined as R assume that R~ N(μ, o²) where μ = 0 and o² = 0.1. = In (st). In this question, (i) Show that R = eR 1. (ii) Calculate VaR0.95 for an investment of £150. Remember that if X~ N(μ,0²) then exis lognormally distributed with parameters and o2. You may use that for a standard normal random variable -¹(0.05) = -1.6449, where & denotes the CDF.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 2EA
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Transcribed Image Text:5. Suppose we have a risky asset with random return R. We have defined R to be,
S₁ - So
So
R =
In
=
Now we introduce the log-return, which is defined as R =
assume that R~ N(u, o²) where μ = 0 and o² = 0.1.
µ
(i) Show that ReR - 1.
=
So
In this question,
(ii) Calculate VaR0.95 for an investment of £150. Remember that if X ~ N(μ,0²)
then ex is lognormally distributed with parameters μ and o². You may use that
for a standard normal random variable Þ−¹(0.05) = −1.6449, where Þ denotes the
CDF.
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