Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate. Ignore credit risk.
A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct?
(i) buy call options on live cattle.
(ii) buy put options on live cattle.
(iii) sell call options on live cattle.
Select the most correct response:
A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in one year?
The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.
Which of the below statements about the arithmetic and geometric average GDR is NOT correct?
Question 730 DDM, income and capital returns, no explanation
A stock’s current price is $1. Its expected total return is 10% pa and its long term expected capital return is 4% pa. It pays an annual dividend and the next one will be paid in one year. All rates are given as effective annual rates. The dividend discount model is thought to be a suitable model for the stock. Ignore taxes. Which of the following statements about the stock is NOT correct?
Question 734 real and nominal returns and cash flows, inflation, DDM, no explanation
An equities analyst is using the dividend discount model to price a company's shares. The company operates domestically and has no plans to expand overseas. It is part of a mature industry with stable positive growth prospects.
The analyst has estimated the real required return (r) of the stock and the value of the dividend that the stock just paid a moment before ##(C_\text{0 before})##.
What is the highest perpetual real growth rate of dividends (g) that can be justified? Select the most correct statement from the following choices. The highest perpetual real expected growth rate of dividends that can be justified is the country's expected:
Question 794 option, Black-Scholes-Merton option pricing, option delta, no explanation
Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European call option?
Where:
###d_1=\dfrac{\ln[S_0/K]+(r+\sigma^2/2).T)}{\sigma.\sqrt{T}}### ###d_2=d_1-\sigma.\sqrt{T}=\dfrac{\ln[S_0/K]+(r-\sigma^2/2).T)}{\sigma.\sqrt{T}}###A stock, a call, a put and a bond are available to trade. The call and put options' underlying asset is the stock they and have the same strike prices, ##K_T##.
Being long the call and short the stock is equivalent to being:
Question 898 comparative advantage in trade, production possibilities curve, no explanation
Adam and Bella are the only people on a remote island. Their production possibility curves are shown in the graph.
Assuming that Adam and Bella cooperate according to the principles of comparative advantage, what will be their combined production possibilities curve?
Question 956 option, Black-Scholes-Merton option pricing, delta hedging, hedging
A bank sells a European call option on a non-dividend paying stock and delta hedges on a daily basis. Below is the result of their hedging, with columns representing consecutive days. Assume that there are 365 days per year and interest is paid daily in arrears.
Delta Hedging a Short Call using Stocks and Debt | |||||||
Description | Symbol | Days to maturity (T in days) | |||||
60 | 59 | 58 | 57 | 56 | 55 | ||
Spot price ($) | S | 10000 | 10125 | 9800 | 9675 | 10000 | 10000 |
Strike price ($) | K | 10000 | 10000 | 10000 | 10000 | 10000 | 10000 |
Risk free cont. comp. rate (pa) | r | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 |
Standard deviation of the stock's cont. comp. returns (pa) | σ | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 |
Option maturity (years) | T | 0.164384 | 0.161644 | 0.158904 | 0.156164 | 0.153425 | 0.150685 |
Delta | N[d1] = dc/dS | 0.552416 | 0.582351 | 0.501138 | 0.467885 | 0.550649 | 0.550197 |
Probability that S > K at maturity in risk neutral world | N[d2] | 0.487871 | 0.51878 | 0.437781 | 0.405685 | 0.488282 | 0.488387 |
Call option price ($) | c | 685.391158 | 750.26411 | 567.990995 | 501.487157 | 660.982878 | ? |
Stock investment value ($) | N[d1]*S | 5524.164129 | 5896.301781 | 4911.152036 | 4526.788065 | 5506.488143 | ? |
Borrowing which partly funds stock investment ($) | N[d2]*K/e^(r*T) | 4838.772971 | 5146.037671 | 4343.161041 | 4025.300909 | 4845.505265 | ? |
Interest expense from borrowing paid in arrears ($) | r*N[d2]*K/e^(r*T) | 0.662891 | 0.704985 | 0.594994 | 0.551449 | ? | |
Gain on stock ($) | N[d1]*(SNew - SOld) | 69.052052 | -189.264008 | -62.642245 | 152.062648 | ? | |
Gain on short call option ($) | -1*(cNew - cOld) | -64.872952 | 182.273114 | 66.503839 | -159.495721 | ? | |
Net gain ($) | Gains - InterestExpense | 3.516209 | -7.695878 | 3.266599 | -7.984522 | ? | |
Gamma | Γ = d^2c/dS^2 | 0.000244 | 0.00024 | 0.000255 | 0.00026 | 0.000253 | 0.000255 |
Theta | θ = dc/dT | 2196.873429 | 2227.881353 | 2182.174706 | 2151.539751 | 2266.589184 | 2285.1895 |
In the last column when there are 55 days left to maturity there are missing values. Which of the following statements about those missing values is NOT correct?