Question

Stock return r_stock is either +2500% or -100% with equal probabilities. Find:

E[r_stock] =

Var[r_stock] =

std_stock=

Is such stock attractive? Would you like to invest everything in this stock?

What is the probability to survive after 2 periods of investing ALL your wealth into it?

How should one approach instruments like that?

Answer 1

Expected Stock Return E[r_stock] = 0.5* 2500%+ 0.5* (-100%) = 1200%

Var[r_stock] = 0.5* (25-12)^2+ 0.5* (-1-12)^2

=169

std_stock = square root of variance = 169^0.5 = 13 or 1300%

The stock is highly risky and thus may be attractive onnly to the highly risk seeking person.

It is not recommended for investment as there is a 50% probability that the entire capital will be lost (loss of 100%)

After 1st period of investing there is a 50% probability that the stock gives 2500% return and 50% probability that the stock gives -100% return (all investment becomes zero)

In case after the 1st period (prob = 0.50) the stock gives +ve return, in the 2nd period also , there is equal probability of stock giving +ve and -ve returns (prob 0.25 ) each

So, total proabability of survival (investment not becoming zero) is only when stock gives +ve return in both periods i..e 0.5*0.5 = 0.25 or 25%

These instruments are better to avoid as they may lead to a loss in capital and are highly risky. If one's risk appetite is very high, one can invest a small part of wealth in these instruments , but NEVER the full wealth.