The equation 1 mi = 5 , 280 ft is true, while the equation 1 yd = 1 m is false. Multiply both sides of each equation by zero. Explain why multiplying both sides of a conditional equation by zero is a bad idea when trying to find the solution.
The equation 1 mi = 5 , 280 ft is true, while the equation 1 yd = 1 m is false. Multiply both sides of each equation by zero. Explain why multiplying both sides of a conditional equation by zero is a bad idea when trying to find the solution.
The equation
1
mi
=
5
,
280
ft
is true, while the equation
1
yd
=
1
m
is false. Multiply both sides of each equation by zero. Explain why multiplying both sides of a conditional equation by zero is a bad idea when trying to find the solution.
1 (Expected Shortfall)
Suppose the price of an asset Pt follows a normal random walk, i.e., Pt =
Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²).
Po+r1+.
⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price
in T days, i.e., VaRq(Pt – Pt–T).
-
• If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution)
Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47).
What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3?
What is P(rt (4) < 2)?
What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13?
• What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given
rt-2 = 0.6?
3 (Sharpe-ratio) Suppose that X1, X2,..., is a lognormal geometric random
walk with parameters (μ, o²). Specifically, suppose that X = Xo exp(rı +
...Tk), where Xo is a fixed constant and r1, T2, ... are IID N(μ, o²). Find
the Sharpe-ratios of rk and log(Xk) — log(Xo) respectively, assuming the
risk free return is 0.
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