Question

1. using only content learned in this unit, describe the steps you would take to insure your investments.

t /4

1. you are to compare buying stock and call options. to do so you are to consider two alternatives.

portfolio a: buying 100 shares of lets go inc. (currently at $57.00). calculate the
total purchase cost - you may ignore commission.
portfolio b: use the total purchase cost to invest in jun $45 call options on lets
go inc. with the premium of $13.75 - remember you are buying contracts and
you may ignore commission.

• you sell your shares from june at a price of $78.
• alternatively, in june you exercise your call option as the current lets go inc. stock is trading at $78.00.

calculate the profit/loss and roi (based on initial investment) on each portfolio (you may ignore
commissions). a /6
which one made (lost) more money? k /1
explain which portfolio is the riskier investment. t /3

Explanation:

Step1: Calculate total purchase cost for Portfolio A

The formula for total cost of stocks is \( \text{Total Cost}=\text{Number of shares}\times\text{Price per share}\).
For Portfolio A, number of shares \(n = 100\), price per share \(P=\$57\). So, \(\text{Total Cost}_A=100\times57=\$5700\)

Step2: Calculate profit for Portfolio A

The formula for profit of stocks is \( \text{Profit}=\text{Number of shares}\times(\text{Selling price}-\text{Purchase price})\).
Selling price \(S = 78\), purchase price \(P = 57\). So, \(\text{Profit}_A=100\times(78 - 57)=\$2100\)

Step3: Calculate ROI for Portfolio A

The formula for ROI is \( \text{ROI}=\frac{\text{Profit}}{\text{Initial Investment}}\times100\%\)
\(\text{ROI}_A=\frac{2100}{5700}\times 100\%\approx 36.84\%\)

Step4: Calculate number of call - option contracts for Portfolio B

Each call - option contract is for 100 shares. The premium per option \(C=\$13.75\). The initial investment is the same as Portfolio A (\(I = 5700\)).
The number of contracts \(N=\frac{\text{Initial Investment}}{\text{Premium per contract}}\), since premium per contract \(=13.75\times100=\$1375\)
\(N=\frac{5700}{1375}\approx 4.14\). But we can only buy whole contracts, so \(N = 4\) (since \(4\times1375=\$5500\) and \(5\times1375=\$6875>5700\))

Step5: Calculate profit for Portfolio B

The formula for profit of call - options is \( \text{Profit}=\text{Number of contracts}\times100\times(\text{Stock price at exercise}-\text{Strike price}-\text{Premium per share})\)
Strike price \(K = 45\), stock price at exercise \(S = 78\), premium per share \(c=\frac{13.75}{100}=0.1375\) (since premium per contract \(=13.75\) for 100 shares)
\(\text{Profit}_B=4\times100\times(78 - 45-13.75)=4\times100\times19.25=\$7700\)

Step6: Calculate ROI for Portfolio B

\(\text{ROI}_B=\frac{7700}{5500}\times 100\% = 140\%\)

for risk:
Call - options (Portfolio B) are riskier. In the case of call - options, if the stock price at expiration is less than or equal to the strike price (\(S\leq K\)), the investor loses the entire premium (in our case, if \(S\leq45\), Portfolio B loses \(\$5500\)). For stocks (Portfolio A), the maximum loss is when the stock price goes to \(0\), but the loss is \(5700\) (the initial investment). However, the leverage in options (small initial investment can lead to large losses or gains) makes Portfolio B riskier.

Answer:

Portfolio A		Portfolio B
ROI	\(36.84\%\)	ROI	\(140\%\)

Portfolio B made more money.