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Q1. Bonds

According to Sullivan, Arthur, Steven and Sheffrin (2003), a bond is a loan that investors offer to firms, government or a municipality. The investors earn interest periodically until the maturity of the bond and the borrower pays the bond on maturity. Bonds have minimal risks as there is the guarantee of a stream of interest at specified date for the duration of the bond to maturity. Compared to the stock market, bonds have their particular risk associated with interest rates fluctuations. They are bought or sold in an open market.

(a) Record of the main parameters of the bonds.

Examples of bonds from London Stock Exchange (fixed coupon rates only)

Coupon rate

Par value

Selling price

Maturity period

i.Brunt wood investments plc

ii. AVIVA plc

iii. B.A.T International finance plc.

iv. Safeway plc.

v. Burford Capital plc

vi. Beazley plc.

vii. Barclays

Viii. Ashford plc (hypothetical)

(b) Calculating yields:

Current yields = annual interest payment / current market price of the bond

(i) Brunt wood Investments plc= 6%*100/104.75 = 5.73%

(ii) AVIVA plc. = 6.125%*100/99.28 = 6.17%

(iii) B.A.T international finance plc. =6.375%100*116.15 = 5.49%

(iv) Safeway plc, = 6.125%*100/108.15 = 5.66%

(v) Burford Capital plc = 6.5%100/103 = 6.32%

(vi) Beazley plc. = 5.375%100/103.62 = 5.19%

(vii) Barclays = 5.75%100/106.5 = 5.4%

(viii) The hypothetical case, Ashford plc. = 6%100/100 = 6%

(c) Supportive statements:

(i) Bonds with the coupon rate less than YTM will be priced at a discount

This is evidenced by AVIVA plc, which has a lesser coupon rate than the yield. The bond is said to be priced at a discount since the market selling price is less than the bond’s par value.

(ii) Bonds with the coupon rate greater than the yield will be priced at a premium

Apart from AVIVA plc, the rest bonds have a coupon rate greater than the yield to maturity. Their market price is greater than their par value hence priced at the premium.

(iii) Bonds with the coupon rate equal to the yield to maturity will be priced at the face value

(d) Durations of bonds

Example of a bond

Duration in years

i.Brunt wood investments plc

ii. AVIVA plc

iii. B.A.T International finance plc.

iv. Safeway plc.

v. Burford Capital plc

vi. Beazley plc.

vii. Barclays

Viii. Ashford plc (hypothetical)

(e) Verifications;

Other things being equal, bonds with a higher coupon rate have a shorter duration. This is because the higher the rate of discounting cash inflows the higher the net present value to offset the price of the bond, hence the shorter duration. This is also the case with a higher yield to maturity. Bonds with a longer time to maturity has a low interest rate and therefore, the longer the duration.

Using a hypothetical bond (Ashford plc) with coupon rate equal to yield to maturity, the par value is equal to the market selling price and, therefore, will be priced at the face value.


Mortgages are types of loans borrowed to own property or land. A mortgage is a type of collateralized loan the security being the value of the property or land in question according to Cortesi (2003). . Various commercial banks offer mortgages and borrowers can borrow directly from the banks. However, borrowers may opt to use brokers or financial advisors in comparing different rates of mortgages from commercial banks. Apart from the security, borrowers are required to pay an initial deposit towards the property they are willing to buy.

(a) A loan of £500,000 for five years will be preferred for an interest rate of 2.25%. (see the workings on Excel Q2.(a)

Original Principal 500000 500000 500000

Loan period 5 5 5

Annual interest rate 2.65% 3.13% 2.25%

Payments per year 12 12 12

Monthly payments £8,906.79 £9,013.26 £8,818.67

(b) A loan of £500,000 for twenty-five years will be preferred for an interest rate of 2.25% (Workings on Excel Q2. (b)

Original principal £500000 £500000 £500000

Loan period 25 25 25

Annual interest rate 2.65% 3.13% 2.25%

Payments per year 12 12 12

Monthly payments £2,281.04 £2,405.00 £2,180.65

(c) Working with Excel (Q2.c)

Original principal £500000 £500000

Loan period 5 25

Annual interest rate 3.29% 3.29%

Payments per year 12 12

Monthly payments £9,048.93 £2,447.16

(d) Barclays Bank has cheaper mortgages compared to HSBC Holdings Plc.

(e) For a loan repayment of 5 years, Barclays Bank is preferable with an initial interest rate of 2.25%, and also preferable for 25 years loan repayment with an initial interest rate of 2.25%.

Q3. Portfolio analysis

A portfolio is a combination of investment tools that are managed together to achieve certain objectives of investors. According to Jones and Charles (2010), portfolio management seeks to prioritize investments and ranking them according to the desired level of returns putting into considerations the inherent risks associated with investments decisions. Portfolio management is crucial to organizations in resource allocation to achieve profitable returns on various types of investments. Portfolio management enables organizations to diversify risks on investments.

(f) Estimating expected returns of the stock portfolio

Security Amount invested (£) Expected return (%)

Part oil 15,000 15

Kit chemical 10,000 16

Amount invested Weight (%) Actual return(%)

Part oil £15000 60 15

Kit chemical £10000 40 16

Total £25000

Expected return

Part oil 0.6 0.15 0.09

Kit Chemical 0.4 0.16 0.064

Expected return (%) 15.4

The portfolio has an expected return of 15.4% as seen in the workings.

(g) Variances and standard deviations of the two returns

Weights Deviation Squared

Part oil 0.6 -0.4 0.16 0.096

Kit Chemical 0.4 0.6 0.36 0.144

Variance 0.24

Standard deviation 0.489898

The portfolio has a variance of 0.24 and a standard deviation of 0.49.

(h) Covariance of the two stocks

Covariance = sum of (return on part oil – average part oil)*(return on kit chemical –

Average kit chemical)/ (Sample size-1)

(i) Correlation coefficient = Cov (rx, ry)/ standard deviation of x & y

= 0.24/ 0.49

(j) Efficient frontier of the portfolio with the two stocks.

An efficient frontier is plotted with expected return on the y-axis and standard deviation on the x-axis.


(k) The minimum variance portfolio of the two stocks has an expected return of 15%.

(l) The expected return is 15.4% as shown in the efficient frontier while the minimum variance of the portfolio is (-0.4)^2 = 0.16

(m) Optimal portfolio of the two stocks has an expected return of 16% with a standard deviation of 0.6.

(n) Expected return of the optimal portfolio is 16% with a risk of 0.6/0.36 = 1.67

Q4.Value at Risk (VaR)

Value at Risk is a technique used to determine the assets required to offset a possible risk, Paul et al. (2005). According to Holton and Glyn (2014), a loss greater than the VaR is referred to as the ‘VaR break.’ The loss is made observable with an assumption that there exist no trading and normal markets and restricting loss on daily accounts of securities in a portfolio. VaR makes use of two three parameters i.e. time (usually a day or sometimes ten days), a confidence level (usually 99% and 95%) and the unit of currency.

(a) Value at Risk (VaR) calculations; It involves the following steps;

  • Setting VaR parameters

  • Establishing market value of the different positions

  • Calculation of VaR of each position with the market volatilities

  • Calculation of portfolio VaR with correlations of the variables

VaR = Market value * price volatility

(See calculations in the Excel)

Calculation Comment

5% 95% confidence worst level

4.90% Data set

4.90%*15.4%=0.75% market value volatility

(b) Higher VaR losses with higher volatilities other things being equal because fluctuation of prices increases the chances of making losses hence more risky. Higher VaR losses with tighter criteria, other things being equal because the investor avoids risky investments hence a low VaR


Cortesi GR. (2003). Mastering Real Estate Principals, p. 371

Holton, Glyn A. (2014). Value-at-Risk: Theory and Practice second edition, e-book.

Jones, Charles P. (2010). Investments Principles and Concepts, John Wiley & Sons, Inc.

McNeil, Alexander, Frey, Rüdiger, Embrechts and Paul (2005). Quantitative Risk Management: Concepts Techniques and Tools. Princeton University Press ISBN 978-0-691-12255-7.

Sullivan, Arthur, Steven M. Sheffrin (2003). Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. p.281.ISBN 0-13-063085-3.