Financial Derivatives and Portfolio Management Assignment

This comprehensive finance assignment delves into various aspects of financial management, including portfolio construction, risk analysis, and valuation techniques. It begins with an analysis of market portfolios, calculating standard deviations and applying the Capital Asset Pricing Model (CAPM) t...Read More

Running head: BUSINESS
Business
Name of the Student:
Name of the University:
Authors Note:

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Contents
Answer 1:.........................................................................................................................................2
Part ii:...........................................................................................................................................3
Part iii:.........................................................................................................................................3
Answer 2:.........................................................................................................................................4
Part i:............................................................................................................................................4
Part ii:...........................................................................................................................................5
Part iii:.........................................................................................................................................5
Part iv:..........................................................................................................................................5
Answer 3:.........................................................................................................................................6
Answer 4:.........................................................................................................................................8
Answer 5:.......................................................................................................................................10
Answer 6:.......................................................................................................................................13
Answer 7:.......................................................................................................................................14
Answer 8:.......................................................................................................................................14
Answer 9:.......................................................................................................................................15
Answer 10:.....................................................................................................................................17
Answer 11:.....................................................................................................................................18
Answer 12:.....................................................................................................................................18
References:....................................................................................................................................20

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Answer 1:
Market portfolio
Security Value (₤' millions) Standard deviation % investment
A 40 5% 20%
B 40 10% 20%
C 60 20% 30%
D 60 30% 30%
Thus in order to achieve market portfolio the proportion of investment to be made in A, B, C and
D class securities is 20%, 20% 30% and 30% respectively.
Standard deviation of the portfolio is calculated below:
Security Value
(₤'
millions
)
Standard
deviation
%
investment
Proportionate
standard
deviation
A 40 5% 20% 1.00%
B 40 10% 20% 2.00%
C 60 20% 30% 6.00%

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D 60 30% 30% 9.00%
Standard deviation of the portfolio 18.00%
Thus, standard deviation of the market portfolio would be 18% on the basis of proportionate
standard deviation.
Part ii:
Capital market line equation is showed below:
Where Rf = Risk free rate of return (5%).
SD = Standard deviation (18%)
Rm = Market rate of return (13%)
Security market line equation is showed below:
Re = Rf + Beta x (Rm – Rf)
= 5% + 1.5 x (13% - 5%)
= 5% + 20.25% - 7.5%
Part iii:

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The pension fund should be invested in equity shares that have market rate of return higher than
17%. In order to diversify the portfolio the investors should invest in the both high rate of return
securities as well as low rate of return of securities. The proportion of total investment should be
such that will entail the pension fund to earn 17% return and keep the risk as low as possible.
None of the securities, i.e. A, B, C and D have expected rate of return even close to what the
pension fund requires as expected rate of return thus, the pension fund should be invested in
different securities which have higher rate of return of 17% or more. The standard deviation
would be significantly higher than the average standard deviation of 18% as computed at the
beginning of the document (Barberis et. al. 2015).
Answer 2:
Part i:
Equity portfolios Expected rate of return Standard
deviation
Coefficient
of variation
Premium for risk
1 8% 5% 0.63 160.0%
2 10% 6% 0.60 166.7%
3 15% 8% 0.53 187.5%
4 20% 13% 0.65 153.8%
5 25% 18% 0.72 138.9%

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As can be seen that equity portfolio 3 has lowest coefficient of variation and highest premium for
standard deviation hence, equity portfolio 3 is the best.
Part ii:
No, with current equity portfolios none of the single portfolio or combined portfolios would
enable the committee to earn a 20% return with standard deviation of 10%. The minimum
standard deviation at a return of 20% will be 11%, i.e. investment to earn 15% return from equity
3 and 5% return from equity 2. Standard deviation would be (8% + 6% x 50%) =11%.
Part iii:
Equity
portfolios
Expected
rate of
return
Standard
deviation
Coefficient
covariance
Premium for risk
1 8% 5% 0.63 160.0% 1 8%
2 10% 6% 0.60 166.7% 1 10%
3 15% 8% 0.53 187.5% 1 15%
4 20% 13% 0.65 153.8% 0.84615
4
0.169231
5 25% 18% 0.72 138.9%
Total expected return 50%

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Thus, total expected return would be 50% with 30% standard deviation.
Part iv:
Expected rate of return with equal weightage is calculated below:
Equity
portfolio
s
Expected
rate of
return
Standard
deviation
Weightage
investment
Proportionate
return
1 8% 5% 0.2 0.016
2 10% 6% 0.2 0.020
3 15% 8% 0.2 0.030
4 20% 13% 0.2 0.040
5 25% 18% 0.2 0.050
Expected rate of return 0.156
Expected rate of return of weightage is 15.60%.
Answer 3:
Part i:

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Calculation of yearly returns from the portfolio assuming that 30% funds are invested in Share A
and 70% in market portfolio.
Year Return from share A Return from Market
portfolio
Combine return
2012 1.50 9.80 11.30
2013 2.10 6.30 8.40
2014 1.20 1.40 2.60
2015 1.80 10.50 12.30
2016 0.30 3.50 3.80
2017 (0.90) (4.20) (5.10)
2018 1.20 4.90 6.10
Part ii:
Calculation of average rate of return and standard deviation based on the 30% weightage in share
A and 70% in market portfolio is calculated below:
Average expected rate of return (39.40 /7) 5.6
3%
Standard deviation 5.15%

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Part iii:
Calculation beta of stock A is provided below:
Year Return from share A Return from Market portfolio
2012 1.50 9.80
2013 2.10 6.30
2014 1.20 1.40
2015 1.80 10.50
2016 0.30 3.50
2017 (0.90) (4.20)
2018 1.20 4.90
7.20 32.20
Average return 1.03 4.60
Beta of stock A (1.03/4.60) 0.22
Answer 4:
Bond Market value

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A 50 55.55556
B 100 111.1111
C 50 55.55556
D 100 111.1111
E 200 222.2222
500 555.5556
Current Macaulay duration (555.5556 / 500) 1.111111
Current Macaulay duration is 1.11.
Modified duration = (1.11 /1+10%)
= 1.11 / 1.10
= 1.0101
Part ii:
The approximate value of the portfolio is calculated below:
Bond Market value Portfolio
value
A 50.00 55.56

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B 100.00 111.11
C 50.00 55.56
D 100.00 111.11
E 200.00 222.22
Approximate value of the portfolio 555.56
Part iii:
In such case the bond manager should issue new bonds at low coupon rate to discharge the old
bonds issued at higher coupon rates.
Answer 5:
Part i:
Bond 1
Year Cash flow Period X cash flow PV Factor @10% pa Present value of inflow
1 9 9 0.909091 8.181818182
2 9 18 0.826446 14.87603306
3 9 27 0.751315 20.28549962
4 9 36 0.683013 24.58848439
5 9 45 0.620921 27.94145954

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6 9 54 0.564474 30.48159222
7 9 63 0.513158 32.32896145
8 109 872 0.466507 406.7944355
565.478284
Macaulay Duration (565.478 / 100) 5.65478284
Part ii:
In case bond yields rise by 1% then both bond 2 and 3 shall be sold to release the funds as the
rate of coupon is significantly less than the yield to maturity in both bond 2 and 3.
Part iii:
In that case it would be better to invest in Bond 1 as it has proportionately higher coupon to yield
to maturity rate as compared to Bond 2. Hence, with boom in yield to maturity it would be better
to invest in bond 1 than bond 2 (Zabarankin, Pavlikov and Uryasev, 2014).
Part iv:
Expected percentage of price change in Bond 3 with credit rating upgrade resulting in reduction
in yield to maturity 13% is calculated below.
Year Cashflow PV Present

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factor
@14.5%
value
1 10 0.873362 8.733624
2 10 0.762762 7.62762
3 10 0.666168 6.661677
4 10 0.581806 5.818058
5 10 0.508127 5.081273
6 10 0.443779 4.437793
7 110 0.38758 42.63382
Value of the bond @14.5% yield 80.99387
Year Cashflow PV
factor
@13%
Present
value
1 10 0.884956 8.849558
2 10 0.783147 7.831467
3 10 0.69305 6.930502
4 10 0.613319 6.133187

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5 10 0.54276 5.427599
6 10 0.480319 4.803185
7 110 0.425061 46.75667
Value of the bond @13% yield 86.73217
Change in price (86.73-80.99) 5.7383
Expected percentage change in
price (5.7383 x 100/80.99)
7.08%
Answer 6:
Part (i):
The fair value of the stock will be calculated using following formula:
P = Dividend at the end of year 1 / (Cost of capital - growth rate)
= ₤11.20.
Workings:
Cost of equity as per CAPM model,
Risk free rate + beta x Market risk premium.
=18%

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Annual growth rate = 12%
Dividend at the end of year 1 = 60 x 112% = 67.20 pence.
Part (ii):
The fair value of the stock at the end of year 3 would be ₤6.48 and the fair value of the stock at
the end of year 4 would be ₤6.81.
Part (iii):
In case the projections prove to be wrong and the stock grows only at 10% per year for 5 years
and then falls to 4% for indefinitely then the stock will be over paid if these are purchase at fair
value calculated in part (i).
Answer 7:
Part (i):
The purchase of such contract implies that only the difference between the interest rate
shall be used to settle the contract between the two parties on the notional principal amount.
Thus, there would be no exchange of principal amount only the difference between interest rates
shall be used for settlement.
Part (ii):
In case the three months interest rate would be 4% then it would be financially beneficial
to sale the contract as it has higher rate of interest as compared to the 4% rate of interest.
Expected profit would be as following:
Expected profit {1000000 x (6% - 4%)} ₤20,000

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Part (iii):
By entering into a forward contract to hedge the rate of interest at 4% will be a best
option to ensure that the risk of fluctuation in the interest rate in the future
Answer 8:
Part i:
As per Black Scholes model the value of share is calculated below:
The fair value is ₤7.57.
Part ii:
Using the following formula:

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The value of share would be ₤8.84
Answer 9:
Part i:
US $ value in 270 days
100000 120000 5326.027 125326
UK pound sterling value in 270 days
100000 100000 1479.452 101479.5
Future price 1.234989
Part ii:
US $ value in 270 days
100000 120000 5326.027 125326

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UK pound sterling value in 270 days
100000 100000 1479.452 101479.5
Sale proceed in pound after
270 days
104438.4
Less: repayment of Pound
in 270 days
101479.5
Profit in 270 days 2958.904
Part iii:
a. The US $ shall be sold immediately if the expected future exchange rate is going to be $1.40/₤1.
b. Profit in dollars is calculated below:
US $ value in 270 days
100000 120000 5326.027 125326
UK pound sterling value in 270 days
100000 100000 1479.452 101479.5
Future price 1.234989
Sale proceed in
pound after 270 days
104438.4

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Less: repayment of
Pound in 270 days
101479.5
Profit in 270 days 2958.904
Profit in dollars 3654.215
c. The loss will be $695 in case the initial assessment is wrong.
Answer 10:
Part (i):
Dividend yield is higher that the risk free rate of interest as each point equals to ₤10. Thus, there
is a dividend return of (50 x 10) =₤500 which is significantly higher than the risk free rate of
interest.
Part (ii):
By purchasing put option to sale the stock at a price higher than the loss margin that the investor
is willing to accept will help the investor to manage the risk of significant loss in the stock
market.
Part (iii):
Speculative strategy to use put option and by using hedging instrument the investor can reduce
the risk of losing his investment due to sudden fall in the stock index.
Answer 11:
Expected rate of return on equity
Debt / equity ratio p 10% p
20
p 30%

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%
0.5 7 27 47
1.5 2.333333 9 15.66667
2 1.75 6.75 11.75
From the above it is clear that the debt to equity ratio affects the rate of return on equity. The
higher the debt to equity ratio the lower would the expected rate of return on equity.
Answer 12:
Part (i):
Beta denotes the volatility of a stock or investment option. Thus, it can also be used to measure
risk in investment.
Part (ii):
The SML is depicted below:
Part (iii):
The shares lying under SLM is overvalued.

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References:
Barberis, N., Greenwood, R., Jin, L. and Shleifer, A., 2015. X-CAPM: An extrapolative capital
asset pricing model. Journal of financial economics, 115(1), pp.1-24.
Zabarankin, M., Pavlikov, K. and Uryasev, S., 2014. Capital asset pricing model (CAPM) with
drawdown measure. European Journal of Operational Research, 234(2), pp.508-517.