$1\mathrm{.}1$ All products traded on the commodity derivative market of the JSE Limited can be physically settled at expiry in fulfilment of a futures contract. You purchase a gold futures contract with an initial margin requirement of $15\%$ and a futures price of R$115250.$

a$)$ What is the alternative to commodity futures if you do not want physical settlement?

b$)$ What would be the key differences if you wanted to purchase gold forwards rather than futures?

c$)$ If the futures price falls to R$108200,$ what will be the percentage loss on your position?

$1\mathrm{.}2$ You purchased four Sibanye Stillwater Limited put contracts for a premium of R$1\mathrm{.}40.$ Sibanye Stillwater Limited is a multinational mining and metals processing company with a share price of R$25\mathrm{.}20$ on the JSE. What is your maximum possible profit? Assume each contract is for $100$ shares.

$1\mathrm{.}3$ On $10$ November $2023,$ an investor buys a call option to purchase the Glencore Pie share at a price of R$6\mathrm{.}30$ with an exercise price of R$58$ on $10$ January $2024.$ Glencore Pie is a Swiss multinational commodity trading and mining company with headquarters in Baar, Switzerland. Assume that the fair value of the share option on $31$ December $2023$ increased to R$22\mathrm{.}50.$

a$)$ At what share price will the investor break even on the purchase of the call?

b$)$ If the share price of Glencore Pie is R$75$ on $31$ December $2023,$ how much will the intrinsic value and time value on the call option be$?$

C$)$ What are the three variables or inputs in the valuation of the option that would have resulted in the share option increasing?

$1\mathrm{.}4$ Refer to the Treasury bond with a par value of R$1000$ maturing on $15$ May $2024$ in the figure below.

a$)$ How much would an investor receive to sell one of these bonds?

b$)$ How much would you receive as a coupon if coupon payments on this bond are semi$-$annual?

c$)$ What is the current yield of the bond?

How much was the closing asked price of the bond the night before?

$3\mathrm{.}1$ Below is a R$100000$ T$-$bill on a dealer's trading platform:

a$)$ How much would the dealer be willing to pay to you if you had this T$-$bill?

b$)$ Calculate the bond$-$equivalent yield $($asked yield$)$ of this T$-$bill.

$3\mathrm{.}2$ You manage an equity fund with an expected risk premium of $10\%$ and a standard deviation of $14\%.$ The rate on Treasury bills is $6\%.$ Your client chooses to invest R$?0000$ of her portfolio in your equity fund and R$30000$ in a T$-$bill money market fund.

a$)$ What are the expected return and standard deviation of your client's portfolio.

b$)$ What is the reward$-$to$-$volatility $($Sharpe$)$ ratio for the equity fund?

c$)$ What do you think would happen to the expected return on shares if investors perceived an increase in the volatility of stocks?

$3\mathrm{.}3$ The price of a share is currently R$200,$ and your time horizon is three years. You expect the cash dividend during the first year to be R$8$ and is expected to grow at $6\%$ per annum. Suppose your best guess is that the price of the share at the end of each year will be R$210,$ R$220$ and R$230.$ What would be the holding period return for each of the three years and the arithmetic average over the three years?