Question

if a stock price today is 100. Every day it can go up or down by 10% with probability 0.5. What is this stock’s 4-days VaR with 5% confidence?

Answer 1

Given that, current price of stock = $100

Every day it can go up or down by 10% with probability 0.5

So, calculating daily standard deviation first.

expected return u = p1*x1 + p2*x2 = 0.1*0.5 - 0.1*0.5 = 0

So, Variance =(1/2)*((u-x1)^2 + (u-x2)^2) = (1/2)*((0 - 0.1)^2 + (0 +0.1)^2) = 0.01

So, daily standard deviation = Variance^0.5 = 0.01^0.5 = 0.1 or 10%

So, 4-day standard = daily standard deviation*(t^0.5) = 10*4^(0.5) = 0.20 or 20%

For a 5% confidence, Z = 1.65

So, 4-day VAR with 5% confidence = 4-day standard deviation*Z*value of stock = 0.20*1.65*100 = $33

So, stock’s 4-days VaR with 5% confidence = $33