BUS329 Financial Markets and Investment Strategies - Final Exam

This document presents a comprehensive solution to a final exam paper for a finance course (BUS329) from S1/TJD 2020. The paper delves into the informational role of financial markets during the COVID-19 pandemic, analyzing market volatility and investor sentiment. It explores concepts such as deferring consumption, short selling strategies, and margin calls in stock trading. The solution also covers capital allocation lines, optimal investment choices, and the independence of portfolio choice tasks. Furthermore, it includes calculations for risk-free rates and options strategies in volatile markets, providing detailed explanations and examples for each concept. The paper aims to assess the student's understanding of financial market dynamics and investment principles.

Final exam paper
BUS329, S1/TJD 2020
(1)(a) How would you evaluate the informational role of financial
market during the recent COVID-19 pandemic around the globe? (6
Marks)
Part a:
The financial markets during the spread of COVID 19 have been going through a series of
volatile movements. The informational role of the financial market implies that the investor’s
sentiment towards the economy is highlighted by the movements in the market. If the economy is
expected to boom in the future or certain company is expected to be profitable, it would lead to rise
in the price of the share of that company. Also when the economy is expected to fall the financial
markets tend to fall or crash highlighting the slow-down in the economy.
At the start of the pandemic the financial markets were very volatile highlighting the lack of
faith among the investors. The sudden impact of COVID 19 reduced the investor confidence towards
the market, which led to the severe fall in the global markets which was subsequently followed by
recovery. However, with the passage of time the information became clear regarding to the slow-
down in the economy. Thus as per the current trend in the global markets the information provided
by the markets is the economic recession is impacting most of the company. This would lead to lay
off by the company and hence rise in unemployment.
(1) (b) Can you transfer/defer your today’s consumption into the future?
Explain the mechanism of how this can be done (4 marks)
Today’s consumption for products and services can be deferred to the future as the money which
would had been spent on the consumption is saved. This means the consumption is deferred for the
future by saving the money or income. This can be done by saving the money in savings account,
pension account or other types of savings available. The pattern with which this can be done is
highlighted by the following example.
A consumer spends $200 every week by eating outside and for recreational purposes.
However, due to COVID 19 the consumer is deferring the consumption for the future and by saving
the amount. This amount can be saved in savings deposit or other deposit by the consumer. Thus
the present consumption of the consumer is deferred to the future.
(1)

(2) (a) Stock market around the world is affected by COVID-19
pandemic. As an experienced investor you decide to take the
advantage of it. Currently the stock of ABC Ltd. is selling for $40 per
share, which was trading at $45 one week earlier and you are
certain that the price will fall further. To take the advantage of this
downward price momentum you sell short 1000 share of ABC Ltd at
the current market price. You want to make $5000 profit from this
short selling. You place an order with your broker to purchase the
shares at a certain price to cover the position. What type of order
did you place with your broker and at what price? Explain why. (5
marks)
The investor is following the strategy of short sale where the shares are borrowed and sold in the
market. Later the shares are bought by the investor and repaid back to the borrower. The investor
has sold the shares at $40 and the quantity of share is 1000 shares. Hence the amount which is
received by the investor through short sale is $40*1000 = $40000.
In order to benefit from the short sale strategy the investor would need to purchase the
shares at a price lower than $40. If the price increases above $40 the investor would have to
purchase at a higher price which would lead to a loss to the investor. Since the investor wishes to
profit of $5000 from the trading strategy, it would require to purchase the shares at $35 per share.
In this manner the purchase cost of the share would be $35000 ($35*1000), while the sale
value would be $40000. The investor would earn a profit of $5000 on the trade. The type of order
which is placed by the investor with the trader is a limit order and the price at which the limit order
is placed is $35.
(2)

(2) (b) Continue from 2(a) above. You borrowed 1000 shares of ABC
Ltd from your broker and sell short. Initial margin is 50%. Your
broker informs you that a margin call will be issued if your equity
falls below $13,500. How much can the price of ABC Ltd rise before
you get a margin call? What is the maintenance margin in your
account? (3 + 2 = 5 marks)
The calculation of the price till which the share can increase before margin call is given by the
following formula,
margin call price= Short sale value+Initial Margin−Equity Value
no of shares
margin call price= ( $ 40∗1000 ) +( $ 40000∗50 %)−$ 13500
1000
margin call price= $ 60000−$ 13500
1000
margin call price= $ 46500
1000
margin call price=$ 46.5
Thus the price till which the share price rise is $46.5, which means the margin call would
occur when the price of the share has increased by $6.5 ($46.5-$40).
The maintenance margin of the margin account is calculated by using the following formula,
Maintenance Margin %= Margin Account Value−Margin Call
Margin Call ∗100
Maintenance Margin %= ( $ 40∗1000 ) +($ 40000∗50 % )−( $ 46.5∗1000)
($ 46.5∗1000) ∗100
Maintenance Margin %= $ 60000−$ 46500
$ 46500 ∗100
Maintenance Margin %= $ 13500
$ 46500∗100 = 29.03%
(3)

(3) (a) “Capital allocation line (CAL) must always be a straight line” – Is
this statement true? Explain with examples (5 marks)
The capital allocation line is a line which comprises of various portfolio of risk free and risky assets.
The line represents each level of risk along with its corresponding returns which is possible through
the various combination of risk free and risky assets. The slope of the capital allocation line is the
slope of Sharpe Ratio. The Sharpe Ratio is known as the risk reward ratio and it measures the
incremental level of return for each level of risk. This portfolio on the capital allocation line
theoretically represents the efficient portfolio which the investor can invest when borrowing and
lending at the risk free rate.
An example in regards to the capital allocation line be taken where, the risk free rate is
assumed to be 4% while the return from risky asset is 10%. Also the standard deviation of the risky
asset is 6% while that of risk free asset is 0%. The various return and deviation of the portfolio is
calculated and presented below,
Figure 1: Cal
Source: By the Author
0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
CAL
(4)

Figure 2: CAL Graph is a straight Line
Source: By the Author
(5)

(3) (b) Can the proportion of optimal investment in risky portfolio (in
a portfolio of one risk-free asset and one risky portfolio) be different
for different investors? Explain with examples. (5 marks)
The optimal investment can be different for different investors in a risky portfolio because every
investor has a different level of risk tolerance level. Investors can be categorized as risk averse, risk
neutral and risk loving. The risk averse investor is afraid to undertake risky investment and hence the
investment portfolio would consist of risk free investment. While the risk loving investor would
prefer the portfolio which is highly risky and the investor would borrow at the risk free rate and
would invest in the portfolio.
The different optimal portfolio is also due to the different efficient frontier for different
investors. The efficient frontier as per portfolio management theory implies that portfolio which
provide the highest return or the lowest level of risk are plotted. Thus since each investor has a
different level of risk, the efficient frontier would be different which would make optimal investment
different for each investor.
(6)

(4) (a) There are two tasks in portfolio choice problem: (i)
determination of the optimal risky portfolio and (ii) capital
allocation. These two tasks are independent, or one is separate from
the other. Explain why. (5 marks)
The portfolio management theory comprises of allocation of investment in an optimal portfolio
which is efficient for the investor. This optimal portfolio is selected from a set of portfolio which form
the efficient frontier. The portfolio which is optimal for the investor is the tangency portfolio or the
portfolio which forms a tangent with the capital allocation line.
As highlighted the capital allocation line is a straight line which comprises of investment
between risky and risk free assets which provide the highest possible return for each level of risk.
The efficient frontier tends to maximize the return or reduce the risk which is present in the portfolio
of the investors.
The two tasks in the portfolio choice are not independent from each other but are
interdependent. Since the investor can choose any portfolio from the capital allocation line for
investment as per the risk preference but would not be the optimal portfolio. Similarly efficient
frontier highlights the various possibility of investments which can be made by the investors.
However, the investor prefers to maximize the return by lowering the risk. This is possible when the
two task of portfolio management are combined which results in the optimal risky portfolio for the
investor.
(7)

(4) (b) Suppose that the expected return and standard deviation of
stock A are 10% and 5% respectively, while the expected return and
standard deviation of stock B are 15% and 10% respectively.
Returns of stock A and B are perfectly negatively correlated. Also
suppose that it is possible to borrow at the risk-free rate. What must
be the value of the risk-free rate? (5 marks)
The calculation of the risk free rate would require the calculation of the Expected Return and
standard deviation of the portfolio.
Portfolio Return= ( WA∗Return A ) +(WB∗Return B)
Portfolio Return= ( 0.5∗10 % ) +(0.5∗15 %)
Portfolio Return=12.5 %
The portfolio Standard deviation is calculated by using the following formula,
Portfolio risk= √ ( W A2 +S D2 )+ ( W B2+S D2 ) +(1∗WA∗WB∗SD∗SD∗r )
Portfolio risk= √ ( 0. 52+ 5 %2 ) + ( 0.52 +10 %2 ) +(2∗0.5∗0.5∗5 %∗10 %∗−1)
Portfolio risk= √ ( 0. 52+ 5 %2 ) + ( 0.52 +10 %2 ) +(2∗0.5∗0.5∗5 %∗10 %∗−1)
Portfolio risk= √ ( 0.000625 ) + ( 0.0025 ) +(−0.0025)
Portfolio risk= √ ( 0.000625 )=2.5 %
The risk free rate of the portfolio is given by the following formula which is presented
below,
Sharpe Ratio = (Portfolio Return – Risk Free Rate)/ Standard Deviation of Portfolio. Hence assuming
the portfolio to be having a Sharpe Ratio of 2. The risk free rate of the portfolio is,
Risk Free Rate = (Sharpe Ratio* Standard Deviation)-Portfolio Return = (2*2.5%) – 12.5% = 7.5%
Alternative Solution:
Portfolio weights between two risky assets
Weight of Stock A = 10%/(5%+10%) = 0.67
Weight of Stock B = 1-0.67 0.33
Expected Return = (0.67*10%)+(0.33*15%) = 11.65%
Portfolio Risk = SQRT( 0.67^2*0.05^2)+(0.33^2*0.1^2)+(2*0.67*0.33*0.05*0.1*-1) = 0.0005
Sharpe Ratio = (0.1165-Risk Free )/ 0.0005 ------- Equation 1
Sharpe Ratio second Formula
(8)

= (0.1-rf)*0.1^2 – ( 0.15 – rf ) * -0.005= 0.001 – 0.01rf – (-0.00075 – (-0.005rf )) –Part 1
=(0.1-rf)*0.1^2 + ( 0.15 – rf ) * 0.05^2 = 0.001 – 0.01rf + 0.000375 – 0.0025 rf – Part 2
=((0.1-rf) + ( 0.15 – rf ))* -0.005 = (-0.0005 + 0.005rf – 0.00075 + 0.005rf) – Part 3
Sharpe Ratio = Part 1/ Part 2 – part 3
Part 2 – Part 3 = 0.001 – 0.01rf + 0.000375 – 0.0025 rf - (-0.0005 + 0.005rf – 0.00075 + 0.005rf)
=0.001 – 0.01rf + 0.000375 – 0.0025 rf +0.0005 – 0.005rf +0.00075 – 0.005rf
= 0.002625 – 0.0025 rf
Sharpe Ratio = 0.00175-0.015 rf/0.002625 – 0.0025 rf---- equation number 2
Equating the two equations
(0.1165 – rf ) / 0.0005 = 0.00175-0.015 rf/0.002625 – 0.0025 rf
0.1165*(0.002625-0.0025rf) – rf*((0.002625-0.0025rf) = 0.0005*(0.00175-0.015 rf)
=0.000306 – 0.000291 rf – 0.002625rf – 0.0025rf^2 = 0.000000875 – 0.0000075rf
=0.000305 = 0.002924rf+0.0025rf^2 = rf(0.00292+0.0025rf)-0.000305
Rf = 0.000305 = 0.031%
Or Rf = 5%
(9)

(5)(a) As a result of the current COVID-19 pandemic, stock markets
around the globe have become volatile. As an investor you perceive
that the markets are going to experience significant movements in
the near future; however, you are not sure about the direction of
such movements. The markets may go up or go down. In such
uncertain circumstances, what type of option strategy would you
recommend to follow? Explain why. (3 marks)
The markets around the globe have become volatile due to the on-going Pandemic of COVID 19. The
options strategy which can be utilized to benefit from the volatile markets is to use a long Straddle.
This strategy involves the use of put and call options at the same strike price, the investor would be
long both the options. Since the market is expected to be volatile but the direction of volatility is not
certain the investor would be long the options.
Hence if the market is moving upwards the call option is exercised and the investor
generates a payoff, while if the market moves downward put option is exercised. However this
strategy would benefit only when there is significant movement in the market.
(10)

(5) (b) The common stock of the ABC Corporation has been trading
in a narrow range, around $50 per share for months, and you
believe it is going to stay in that range for the next three months.
The price of a 3-month put option with an exercise price of $50 is
$4.
(i) if the risk-free rate is 10% per year, what must be the price of a
3-month call option on ABC stock at an exercise price of $50 if it is
at the money? (Assume put-call parity holds and the stock pays no
dividend). (2 marks)
(ii) What would be a simple option strategy using a put and call to
exploit your conviction about the stock price’s future movements?
Explain clearly. (3 marks) (iii) How far can the stock price move in
either direction before you lose money? (2 marks)
Strike Price $50, Stock price $50, Risk free rate 10% put option price $4. Hence the put call parity is
given by the following formula,
Put price+stock price=call price−Strike price /(1+ Rf )t
$ 4 +$ 50=call price− $ 50
( 1+10 % )( 3
12 )
$ 54−$ 48.82=call price
call price = $5.17
Part ii:
The strategy which can be employed by the investor to generate a profit from the stock
expectation is a short straddle. The investor would sell the call option and the put option at the
strike price of $50. Thus, the investor would receive the premium as income and would expect both
the options to expire out of the money. Thus the investor would benefit from the premium received
by selling the options.
The maximum profit which the investor can generate from this strategy is the amount of the
total premium received. Thus the call premium is $5.17 while the put premium is $4. Hence the total
profit from the strategy for the investor is ($4+$5.17) = $9.17.
The loss from the strategy can be theoretically infinite as the share price can increase or
decrease in either direction .However, the maximum loss which the investor can face in the
downward movement is $50-$4-$5.17 = $40.83
Part iii:
The two break even points for the strategy is calculated below,
Break-even Point 1: Strike Price – Premium Received = $50-$9.17 = $40.83
Break-even Point 2: Strike Price + Premium Received = $50+$9.17 = $59.17.
Thus the investor would be able to profit from this strategy if the stock price remains
between $40.83 - $59.17.
(11)

[END OF EXAM PAPER]
FORMULA SHEET
1. rtaxable= rmuni
(1−t)
2. Net Asset Value= Market value of assets−Liabilities
Shares outstanding
3. Rate of return= NAV 1−NAV 0 + Income∧capital gain distributions
NAV 0
4. rreal= rnom−i
1+i
5. Effective annual rate: EAR= [ 1+r f ( T ) ] 1
T −1
(12)