Question

A big pharmaceutical company, DRlg, has just announced a potential cure for cancer. The stock price increased from $4 to $103 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 2%, quoted as an APR based on a 365-day year. DRlg made up 0.05% of the market portfolio before the news announcement.

a. On the announcement your overall wealth went up by 1.3% (assume all other price changes cancelled out so that without DRlg, the market return would have been zero). How is your wealth invested?
b. Your friend's wealth went up by 24%. How is his wealth invested?
a. On the announcement your overall wealth went up by 1.3% (assume all other price changes cancelled out so that without DRig, 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 decimifi plices.)

Answer 1

Your wealth increased by 1.3% exclusively due to DRig's stock jump, indicating you are 100% invested in the market. Your friend's wealth boost by 24% suggests he might have a leveraged investment in DRig, theoretically exceeding normal investment constraints.

Step-by-step explanation:

We can calculate how much of each person's wealth was invested in DRig by analyzing the change in their overall wealth based on the stock's disproportionate price increase. Since the market return without DRig would have been 0%, the increase in wealth is solely due to the change in DRig's stock price.

For you, the overall wealth increased by 1.3%, and knowing DRig made up 0.05%% of the market portfolio, the percentage of your wealth invested in DRig can be found through the following ratio:

Investment ratio = (1.3% wealth increase) / (2590% stock increase * 0.05% DRig's market weight)

Since the stock increased by (103 - 4) / 4 * 100% = 2475%, we must add the original 100% to find the total percentage change from original value, becoming 2475% + 100% = 2575%. Now, we plug in the values:

Investment ratio = (0.013) / (25.75 * 0.0005) = 1 or 100%

Similarly, for your friend, with a 24%% wealth increase:

Investment ratio = (0.24) / (25.75 * 0.0005) = 18.68852 or 1868.852%

Since one cannot have more than 100% of their wealth in one investment due to leverage constraints in normal conditions, it implies that your friend was using borrowed money to invest in the market, specifically leveraging their investment in DRig. This is a hypothesis because typical leverage would exceed conventional limits.