Question

Suppose that you are trying to decide whether to spend $5,000 on stock issued by WildWeb or on a bond issued by the same company. There is a 30 percent chance hat the value of the stock will rise to $11,000 at the end of the year and a 70 percent chance that the stock will be worthless at the end of the year. The bond promises an interest rate of 30 percent per year, and it is certain that the bond and interest will be repaid at the end of the year Assuming that your time horizon is exactly one year, will you choose the stock or the bond? By how much is your expected end of year wealth reduced if you make the wrong choice? S Suppose the odds of success improve for WildWeb: Now there is a 40 percent chance that the value of the stock will be $11,000 at year's end and only a 60 percent chance that it will be worthless. Should you now choose the stock or the bond?

Answer 1

Answer

Wealth after 1 year If 5000 are invested on the bonds is 5000 + 30% of 5000 = 5000 + 0.3*5000 = 6500

Expected Wealth after 1 year if 5000 are invested on the stock is given by:

E(W) = p₁W₁ + p₂W₂ Here p₁ = 0.3 , W₁ = 11000, p₂ = 0.7 and W₂ = 0

=> E(W) = 0.3*11000 + 0.7*0 = 3300

As , Wealth if invested on Bond > Wealth if invested on Stock.

Hence I will choose Bond

As calculated above E(W) = 3300. If I choose a wrong alternative , My Expected wealth will reduced by 5000 - 3300 = $1700

Similarly as above,

Wealth after 1 year If 5000 are invested on the bonds is 5000 + 30% of 5000 = 5000 + 0.3*5000 = 6500

Expected Wealth after 1 year if 5000 are invested on the stock is given by:

E(W) = p₁W₁ + p₂W₂ Here p₁ = 0.4 , W₁ = 11000, p₂ = 0.6 and W₂ = 0

=> E(W) = 0.4*11000 + 0.6*0 = 4400

As , Wealth if invested on Bond > Wealth if invested on Stock.

Hence I will choose Bond.