Question

Suppose you toss a coin every day for the next 10 years, if tail the return is 1% if head the return is -1%. If you measure the beta of this asset using the S&P as the market index, which scenario has the highest probability to occur?

a. beta=0

b. -0.01<beta<0.01

c. -1<beta<1

d. beta=-1

e. beta=1

Answer 1

b. -0.01<beta<0.01

Beta is a measure of the correlation of the security returns with the index returns. If the stock generally increases with the market index increase, the beta is positive and vice-versa.

In this case, however, the returns are totally uncorrelated with the S&P market index returns as the coin toss is random and it can generate any return not correlated with the market index returns. Due to this the correlation of the returns of the returns with the returns of the market index would be close to zero and hence beta would be close to zero since the sample space is large enough (10 years)