**Question 207** income and capital returns, bond pricing, coupon rate, no explanation

For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?

Let: ##P_0## be the bond price now,

##F_T## be the bond's face value,

##T## be the bond's maturity in years,

##r_\text{total}## be the bond's total yield,

##r_\text{income}## be the bond's income yield,

##r_\text{capital}## be the bond's capital yield, and

##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.

Your main expense is fuel for your car which costs $100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month).

You have $2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change.

Assuming that you have no income, in how many months time will you not have enough money to **fully** refuel your car?

The expression 'cash is king' emphasizes the importance of having enough cash to pay your short term debts to avoid bankruptcy. Which business decision is this expression most closely related to?

A man just **sold** a **call** option to his counterparty, a lady. The man has just now:

A trader **buys** a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.

What is the smallest price change that would lead to a margin call for the buyer?

**Question 711** continuously compounding rate, continuously compounding rate conversion

A continuously compounded **semi-annual** return of **5**% ##(r_\text{cc 6mth})## is equivalent to a continuously compounded **annual** return ##(r_\text{cc annual})## of:

**Question 748** income and capital returns, DDM, ex dividend date

A stock will pay you a dividend of $**2** tonight if you buy it **today**.

Thereafter the annual dividend is expected to grow by **3**% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.

What is the stock price today and what do you expect the stock price to be tomorrow, approximately?

**Question 800** leverage, portfolio return, risk, portfolio risk, capital structure, no explanation

Which of the following assets would you expect to have the highest required rate of return? All values are current market values.