Question

1. Last year at this time, a mutual fund had an NAV of $13.20 per share. Over the past year the fund paid dividends of $0.70 per share and had a capital gains distribution of $1.20 per share. What is the holding period return assuming that the current NAV is $14.42?

• 23.6

• 19.78%

1. What is the fundamental value of a call with a strike price of $30 and a market price of $33?

• $300

• 230

2. Grant purchased one call on XYZ stock at an exercise price of $25. The market price of XYZ stock when Grant purchased the call was $24 a share. XYZ is currently priced at $30 a share. Grant paid $120 to buy the call. How much profit will Grant make if he exercises the option today and then sells the shares? Ignore all transaction-related costs

• $380

• 420

4. The price of ABC stock is currently $42 per share, but in six months you expect it to rise to $50. ABC does not pay a dividend. You buy a six-month call on ABC, with a strike price of $45. The option cost $200. What holding period return do you expect on this call? Ignore transaction costs and taxes

• 150

• 175

Please explain and show work

Answer 1

1. Mutual Fund Return
NAV of the mutual fund at the beginning of the year is given as $13.20 and that at the end of the year is $14.42
Returns from investing in the mutual fund have been in the form of

1. Dividend of $0.70
2. Capital gains distribution of $1.20
3. Unrealized capital gain which is Final NAV - Initial NAV = $14.42 - $13.20 = $1.22

So, the total return from the fund over the one year period = $0.70 + $1.20 + $1.22 = $3.12

Therefore, the holding period return = Total returns during the period invested / Initial NAV = $3.12 / $13.20 = 23.6%

2. Fundamental Value of a Call Option
For the given call option, strike price is $30. Current market price of the underlying stock is $33.

Fundamental value of a call = Current market price - Strike price = $33 - $30 = $3

Usually the contract size (number of shares ) of an option is 100 shares, so the fundamental value is $3 x 100 = $300

3. Profit made by Grant
Strike price of the call option is $25
Current market price of the underlying stock is $30
Price of the option is $120

If Grant exercises the call option today, he would exercise his right to buy 100 shares (option contract size) at $25 and then sell them at market price i.e.$30.

Therefore the gain = current market price - strike price = $3,000 - $2,500 = $500

However, Grant has paid $120 to purchase the option. So his profit from exercising the option = $500 - $120 = $380 (ignoring transaction costs).

4. ABC Stock - Holding period return
This question is similar to the previous one. Here, the strike price is $45. While the stock currently trades at $42, it is expected to trade at $50 six months from now.

Price of the option is $200

When the call option is exercised at the end of six months, 100 shares (contract size) can be bought at $45 and simultaneously, they can be sold at $50 in the market.

Therefore the expected gain = current market price - strike price = $5,000 - $4,500 = $500

However, the price of the option is $200. So the profit from exercise the option = $500 - $200 = $300 (ignoring transaction costs).

Holding period gain = Profit from exercising the option / Price of the option = $300 / $200 = 150%