How should you invest your money so that you have the largest expected gain irrespective of how the election turns out?

Question

You have inherited $10,000 just prior to a presidential election and wish to invest it in solar energy and oil stocks. An investment adviser provides you with a payoff matrix that indicates your probable 4- year gains, depending on which party comes into office. How should you invest your money so that you would have the largest expected gain irrespective of how the election turns out?

                                                       Player C (Fate)
                                              Republican      Democrat
Player R   Solar                             $4000             $3000

you            Oil                              $2000             $5000

 

 

 

The amount you should invest in solar energy is $__________ (round to two decimal places)

The amount you should invest in oil is $__________ (round to two decimal places)

 

Answer 1

I assume you can only buy stocks, and short selling is not allowed.

 

Let S be proportion invested in solar energy, and 1-S be proportion invested in oil.

 

Then (* see below)

if Republicans win, Portfolio return = 0.4S + 0.2(1-S) = 0.2S + 0.2

if Democrats win, Portfolio return = 0.3S + 0.5(1-S) = 0.5 - 0.2S

 

Let p be the probability that Republicans win, then

Expected portfolio return = p(0.2S + 0.2) + (1-p)(0.5 - 0.2S)

Expected portfolio return = 0.2pS + 0.2p + 0.5 - 0.2S - 0.5p + 0.2pS

Expected portfolio return = 0.4pS - 0.3p - 0.2S + 0.5

Expected portfolio return = S(0.4p - 0.2) + 0.5 - 0.3p

 

Now if p = 0.5, Expected portfolio value = 0.25

if p > 0.5, then the coefficient of S is positive, so S = 100% will maximize portfolio return

if p < 0.5, then the coefficient of S is negative, so S = 0% will maximize portfolio return

 

Intuitively, if both Republicans and Democrats are equally likely to win, then it doesn't matter how you split your investment.

If Republicans are more likely to win, then invest completely in Solar energy. Similarly, invest completely in Oil if Democrats are more likely to win.

 

 

Alternatively

if you just want to find the level of S that makes the portfolio return equal regardless of who wins, then just equate both portfolio returns in (*)

0.2S + 0.2 = 0.5 - 0.2S

0.4S = 0.3

S = 0.75

 

So invest 75% in solar energy and 25% in oil

Or $7,500 in solar energy and $2,500 in oil.