Question

You have $20,000 to invest in Company shares that currently trade at $41.40. You choose to invest 30% of your funds in long-term call options with a strike of $45 that are currently quoted at $0.65. The options expire in 11 months. The other funds will be placed in a money market earning 6.5% compounded monthly. What is the rate of return for the holding period on the total investment position if the share price is up 24% at expiry?

Answer 1

Amount Invested in Options = 20000*30% = $6000

Therefore, Amount Invested in Money Market = 20000-6000 = $14000

Number of Options Bought = 6000/0.65 = 9230.77 = 9231 Options(approx)

Price at expiry = Current Price+24% = 41.4+24% = $51.336

Profit on Options = (Price at expiry-Strike Price-Premium)*Number of Options = (51.336-41.4-0.65)*9230.77 = 9.286*9230.77 = $85716.93

Effective Interest Rate for 11 months = [{1+(Interest Rate/12)}^11]-1 = [{1+(0.065/12)}^11]-1 = 0.0612236

Profit on Money Market = 14000*0.0612236 = $857.13

Therefore, Total Profit = 85716.93+857.13 = $86574.06

Therefore, Holding Period Return = Total Profit/Amount Invested = 86574.06/20000 = 4.3287 = 432.87%

Rate of Return for full year = Holding Period Return*12/Holding Period = 432.87*12/11 = 472.22%

Note: The Phase "Rate of Return for the Holding Period" is vague. Generally, "Rate of Return" means Return for FULL YEAR, whereas "Holding Period" means the Period for which Investment is held. Therefore, Rates for Both are calculated.