A big pharmaceutical company, DRIg, has just announced a potential cure for canc

Question

A big pharmaceutical company, DRIg, has just announced a potential cure for cancer. The stock price increased from $5 to $100 in one day. A friend calls to tell you that he owns DRIg. You proudly reply that you do, too. Since you have been friends for some time, you know that he holds the market, as do you, and so you both are invested in this stock. Both of you care only about expected return and volatility. The risk-free rate is 3%, quoted as an APR based on a 365-day year. DRIg made up 0.20% of the market portfolio before the news announcement. a. On the announcement your overall wealth went up by 1.0% (assume all other price changes cancelled out so that without DRIg, the market return would have been zero). How is your wealth invested? b. Your friend's wealth went up by 2.0%. How is his wealth invested? a. On the announcement your overall wealth went up by 1.0% (assume all other price changes cancelled out so that without DRlg, the market return would have been zero). How is your wealth invested? (Round all intermediate values to five decimal places as needed.) The percentage of your wealth invested in the market is %. (Round to two decimal places.)

Explanation / Answer

The return on DRIg on that day = (stock price after increase – stock price before increase)/ stock price before increase * 100

= ($100-$5)/$5 *100 = 1900%

Therefore, if DRIg made up 0.20% of the market and the rest of the market earned 0%,

The return on the market portfolio = 1900%*0.20% + 0% *(1-0.20%)

= 3.80%

We know that the risk-free rate is 3% per year (an APR basis)

Therefore, return per day = 3%/365 = 0.0082192% per day

Assume that percentage of your wealth invested in the market is x and the rest (1 –x) in the risk-free asset if the value of your portfolio went up by 1.0%, then

3.80% * x + (1-x) *0.0082192% = 1.0%

Or x = 26.16%

Therefore percentage of your wealth invested in the market is 26.16%.

b. Assume that percentage of your friend’s wealth invested in the market is y and the rest (1-y) in the risk-free asset if the value of your friend’s portfolio went up by 2.0%, then

3.80% * y + (1-y) *0.0082192% = 2.0%

Or y = 52.53%

Therefore percentage of your friend's wealth invested in the market is 52.53%.

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