Fight Finance

Question 41  DDM, income and capital returns

The following is the Dividend Discount Model (DDM) used to price stocks:

### P_0 = \frac{d_1}{r-g} ###

Assume that the assumptions of the DDM hold and that the time period is measured in years.

Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?

(a) ## d_1(1+g)^3 ##

(b) ## P_3(r-g) ##

(c) ## d_2(1+g)^2 ##

(d) ## P_0(1+g)^3(r-g) ##

(e) ## P_0(1+g)^2(r-g) ##

Question 156  APR, effective rate

A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually.

Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.

(a) 0.024695, 0.05, 0.000136.

(b) 0.025, 0.050625, 0.000137.

(c) 0.029563, 0.06, 0.000162.

(d) 0.03, 0.06, 0.000167.

(e) 0.03, 0.0609, 0.000164.

Question 234  debt terminology

An 'interest only' loan can also be called a:

(a) Discount loan

(b) Par loan

(c) Premium loan

(d) Deferred repayment loan

(e) Fully amortising loan.

Question 630  mispriced asset, NPV, DDM, market efficiency

A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to always be 7% pa and rest is the capital yield.

Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?

In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates.

The answer choices below are given in the same order (15% for 100 years, and 15% forever):

(a) 84,214.90,   Infinite

(b)  2,521.12,   3,000

(c)  2,100.93,   2,500

(d)  1,249.38,   1,333.33

(e)          0,               0

Question 638  option, option payoff at maturity, no explanation

Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.

(a) ##f_{LP,T}=max⁡(S_T-X_T,0)##

(b) ##f_{LP,T}=max⁡(X_T-S_T,0)##

(c) ##f_{LP,T}=-max⁡(S_T-X_T,0)##

(d) ##f_{LP,T}=-max⁡(X_T-S_T,0)##

(e) ##f_{LP,T}=min⁡(X_T-S_T,0)##

Question 670  fixed for floating interest rate swap

A company can invest funds in a five year project at LIBOR plus 50 basis points pa. The five-year swap rate is 4% pa. What fixed rate of interest can the company earn over the next five years by using the swap?

(a) 0% pa

(b) 3.5% pa

(c) 4% pa

(d) 4.5% pa

(e) 5% pa

Question 833  option, delta, theta, standard deviation, no explanation

Which of the following statements about an option (either a call or put) and its underlying stock is NOT correct?

(a) The option’s expected future continuously compounded returns are always more than or equal to the underlying stock’s expected future continuously compounded returns.

(b) The option’s standard deviation of dollar price changes is always less than or equal to the underlying stock’s standard deviation of dollar price changes.

(c) The option’s standard deviation of continuously compounded returns are always less than or equal to the underlying stock’s standard deviation of continuously compounded returns.

(d) As time elapses and the maturity date of an option approaches, its price will fall, all other things remaining equal.

(e) If the underlying stock’s price rises by $0.01, the call option’s price will rise by less than $0.01 and the put option’s price will fall by less than $0.01.

Question 895  comparative advantage in trade, production possibilities curve

Adam and Bella are the only people on a remote island.

Luckily there are Coconut and Date palm trees on the island that grow delicious fruit. The problem is that harvesting the fruit takes a lot of work.

Adam can pick 7 coconuts per hour, 6 dates per hour or any linear combination of coconuts and dates. For example, he could pick 3.5 coconuts and 3 dates per hour.

Bella can pick 3 coconuts per hour, 5 dates per hour or any linear combination. For example, she could pick 1.5 coconuts and 2.5 dates per hour.

This information is summarised in the table and graph:

Harvest Rates Per Hour
	Coconuts	Dates
Adam	7	6
Bella	3	5

 

Which of the following statements is NOT correct?

(a) Adam’s opportunity cost of picking one date per hour is 7/6 coconuts, so he picks around 1.1667 coconuts per one date per one hour.

(b) Bella’s opportunity cost of picking one date per hour is 3/5 coconuts, so she picks around 0.6 coconuts per one date per one hour.

(c) Adam’s opportunity cost of picking one coconut per hour is 6/7 dates, so he picks around 0.8571 dates per one coconut per one hour.

(d) Bella’s opportunity cost of picking one coconut per hour is 5/3 dates, so she picks around 1.6667 dates per one coconut per one hour.

(e) The gradients (rise over run) of the lines in the graph are measured in dates per one coconut per hour.

Question 923  omitted variable bias, CAPM, single factor model, single index model, no explanation

Capital Asset Pricing Model (CAPM) and the Single Index Model (SIM) are single factor models whose only risk factor is the market portfolio’s return. Say a Taxi company and an Umbrella company are influenced by two factors, the market portfolio return and rainfall. When it rains, both the Taxi and Umbrella companies’ stock prices do well. When there’s no rain, both do poorly. Assume that rainfall risk is a systematic risk that cannot be diversified and that rainfall has zero correlation with the market portfolio’s returns.

Which of the following statements about these two stocks is NOT correct?

The CAPM and SIM:

(a) Betas of the Taxi and Umbrella companies will only measure the companies’ sensitivity to the market portfolio risk factor, not the rainfall factor.

(b) Will over-estimate the Taxi and Umbrella stocks’ systematic variance.

(c) Will over-estimate the Taxi and Umbrella stocks’ diversifiable variance.

(d) Models will show positive correlations between the Taxi and Umbrella stock’s residual (also called idiosyncratic) returns.

Question 958  confidence interval, normal distribution

A stock's returns are normally distributed with a mean of 8% pa and a standard deviation of 15 percentage points pa. What is the 99% confidence interval of returns over the next year? Note that the Z-statistic corresponding to a one-tail:

• 90% normal probability density function is 1.282.
• 95% normal probability density function is 1.645.
• 97.5% normal probability density function is 1.960.
• 99% normal probability density function is 2.326.
• 99.5% normal probability density function is 2.576

The 99% confidence interval of annual returns is between:

(a) 61.52% and -61.52% pa.

(b) 56.52% and -36.52% pa.

(c) 51.52% and -51.52% pa.

(d) 46.64% and -30.64% pa.

(e) 30% and -10% pa.