A stock is expected to pay the following dividends:
Cash Flows of a Stock | ||||||
Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
Dividend ($) | 0.00 | 1.15 | 1.10 | 1.05 | 1.00 | ... |
After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
- the dividend at t=5 will be ##$1(1-0.05) = $0.95##,
- the dividend at t=6 will be ##$1(1-0.05)^2 = $0.9025##, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in four and a half years (t = 4.5)?
There are a number of ways that assets can be depreciated. Generally the government's tax office stipulates a certain method.
But if it didn't, what would be the ideal way to depreciate an asset from the perspective of a businesses owner?
Question 488 income and capital returns, payout policy, payout ratio, DDM
Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.
BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.
Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.
Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV.
All things remaining equal, which of the following statements is NOT correct?
A trader sells one crude oil futures contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before expiry then in one year she will have the:
Which of the following quantities is commonly assumed to be normally distributed?
Question 730 DDM, income and capital returns, no explanation
A stock’s current price is $1. Its expected total return is 10% pa and its long term expected capital return is 4% pa. It pays an annual dividend and the next one will be paid in one year. All rates are given as effective annual rates. The dividend discount model is thought to be a suitable model for the stock. Ignore taxes. Which of the following statements about the stock is NOT correct?
What derivative position are you exposed to if you have the obligation to sell the underlying asset at maturity, so you will definitely be forced to sell the underlying asset?
Being long a call and short a put which have the same exercise prices and underlying stock is equivalent to being:
You work for XYZ company and you’ve been asked to evaluate a new project which has double the systematic risk of the company’s other projects.
You use the Capital Asset Pricing Model (CAPM) formula and input the treasury yield ##(r_f )##, market risk premium ##(r_m-r_f )## and the company’s asset beta risk factor ##(\beta_{XYZ} )## into the CAPM formula which outputs a return.
This return that you’ve just found is:
Question 956 option, Black-Scholes-Merton option pricing, delta hedging, hedging
A bank sells a European call option on a non-dividend paying stock and delta hedges on a daily basis. Below is the result of their hedging, with columns representing consecutive days. Assume that there are 365 days per year and interest is paid daily in arrears.
Delta Hedging a Short Call using Stocks and Debt | |||||||
Description | Symbol | Days to maturity (T in days) | |||||
60 | 59 | 58 | 57 | 56 | 55 | ||
Spot price ($) | 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?