Question

Suggest what shape the probability distribution of returns looks like for the following and explain your suggestion (i.e. are they likely to be normal, or positively or negatively skewed? How likely are extreme values versus values close to the average?) : a) Buying bonds issued by a company that is considered a relatively high risk of default. b) A portfolio of shares in a wide range of stocks c) Buying long-term US government bonds at the current historically low yields. These bonds are considered to have a very low probability of default. d) Writing a call option. e) Buying a put option.

Answer 1

a) In this case it will look like negatively skewed as the high risk of default can cause negative returns

b) it will be normal in this case as the portfolio here is a well diversified one and hence normal returns are expected

c) This will be slightly positivity skewed as the long term bonds have very less likely chance of default and current yield is low, so expectations are high for growth

d) Buying a call option hedges against any uprise of price, which means the expectation is that market will go up. So it will be positively skewed.

e) Buying a put option means again you’re expecting the market price to rise and the option will not get exercised. So this will be positively skewed as well.