BEO2431 Business Risk
Q1 Identify and rank risk factors that are considered in financial institutions and non-banking cooperation.
(Maximum only one page with references)
10 Marks
Q2. XYZ Property development Ltd is offered a choice of loan funds at the following nominal interest rates:
(1) 5.52% payable annually
(2) 5.50% payable semi annually
(3) 5.48% payable quarterly
(4) 5.45% payable monthly
Which of these nominal interest rates provides the lowest cost of finance in terms of the corresponding effective annual interest rates?
2-Marks
Q3. XYZ Company is considering three investments to invest $100,000: Bond, Stock mutual fund, fixed deposits:
- The fixed deposits guaranteed to pay 5.5% return.
- Stock mutual fund as 12%, 9% or -2% depending on whether market conditions are: good, average, or poor.
- Bond 10%,8.7% or 3% depending on whether market conditions are: good, average, or poor.
- XYZ company estimated the probability of a good, average, and poor market to be 0.3, 0.5, and 0,2 respectively.
- What decision should be made according to the EMV decision rule?
- What decision should be made according to the EOL (expected opportunity loss) decision rule?
- How much XYZ company should be willing to pay to obtain a market forecast that is 100% accurate.
- Draw a decision tree to this problem
5 Marks
Q4. Share Valuation
ABC Ltd pays annual dividends on its ordinary shares. The latest dividend of 32 cents per share was paid yesterday. The dividends are expected to grow at 3 per cent per year for the next two years, after which a growth rate of 2 per cent is expected to be maintained indefinitely. Estimate the value of one share if the required rate of return is 12 per cent.
3- Marks
Q5 Option Pricing Model
Calculate the value of a three-month call option assuming the current price is $42, the strike price is $40, the risk-free interest rate is 3% per annum ((continuously compounding interest rate), and the volatility (σ2) is 22 % per annum.
4- Marks
Q6. Binomial Option Pricing
One of the bank current share price is $42, and it will be worth either $45 or 38 in two months. The risk free rate of interest is 4% (continuously compounding interest rate). What is the value of call option with an exercise of $43. Find the hedge ratio and explain.
4- Marks
Q7. USE ONLY the CALCULTOR to answer the Following Questions.
Mr. John expects to invest 20 million dollars on ABC and XYZ shares. He found the following annual stock return numbers for the period of 2013 to 2017.
What would be your investment recommendation for Mr. John based on risk and return measurements? (Hint you may have to calculate stock performances using average return, standard deviation, chances of obtaining negative return, geometric mean, cumulative wealth index, VaR (both parametric and non-parametric) and the SHARPE RATIO etc…) 10-Marks
|
Date |
ABC Stock Return |
XYZ Stock Return |
|
2013 2014 2015 2016 2017 |
- 0.49% 0.93% 1.77% 2.18% |
- -2.22% 5.66% 1.82% 0.31% |
Suppose 10 million is invested in ABC stock and 10 million is invested in XYZ stock and calculate the VaR at 5% level of an equally weighted portfolio and compare the result with the individuals’ assets VaR values. Correlation between ABC return and XYZ return is (0.076). Consider Parametric Approach Only.
2- Marks
Covariance Matrix
|
|
RABC |
RXYZ |
RASX200 |
|
RABC |
0.0000442 |
|
|
|
RXYZ |
0.0000145 |
0.000815 |
|
|
RASX200 |
0.0000174 |
0.000161 |
0.0000596 |
(a) Calculate the optimal weights for A and B based on Minimum Risk approach.
3 Marks
(b) calculate the Systematic Risk (β) for share A and Share B and comment on these values
3 Marks Q8. Volatility Forecasting
- Calculate the volatility (σ2) of ABC and XYZ Shares. The parameter l in the exponential weighted moving average (EWMA) σn2= l σn-12 + (1-l) U2n-1- model is 0.96. Forecast the 2018 Volatility of ABC using the 2016 and 2017 share prices 51.80 and 52.93 and Volatility of XYZ using share prices 67.14 and 67.35 with the aid of estimated volatility (σ2) and EWMA model?
3- Marks
- Write the GARCH (1, 1) model. Forecast the 2018 Volatility of ABC and XYZ shares using the 2016 and 2017 prices, estimated volatility and the given parameters of a GARCH (1, 1) model ω= 0.000003, α=0.04, and β=0.82 and ω= 0.000002, α=0.05, and β=0.82.respectively
3… Marks
- Estimate the long-run average volatility of ABC and XYZ and comment on these values 2 marks
Answer:
Q1 Solutions
Risks may be classified as financial and non-financial risks (Actuaries, 2018). Examples of financial risks include:-
- Credit risk- This is the risk where third parties such as borrowers or counterparty defaults on their payments.
- Liquidity risk- This is a risk where an entity do not have enough financial resources to meet their obligations. Banks have a higher liquidity risk in comparison to other institutions, because they lend depositors’ funds and funds raised from money markets to other organizations, for longer periods than they offer to the providers of the funds.
- Market Risk- Movements in investment market values, interest rates and inflation rates may lead to market risk.
- Business risk- These are specific to the business undertaken as a bank, investing in a business or project that fails to be successful.
- Systemic risk -Systemic risk cannot be diversified away. It is usually associated with succession failures such that failure of a big firm may cause the failure to other related entities. e.g. global financial crisis (Gangreddiwar, 2015). Furthermore, it tends to affects the entire industry.
Examples of non-financial risks include:-
- Operational risk – This is an internal risk. It arises from inadequate or failed internal processes, systems and people.
- External risk – This risk is beyond the company’s control as it arises from external events e.g. attacks, fire, tsunamis, regulation changes
References
Actuaries, I. a. (2018). Actuarial Risk Management. London: IFOA.
Gangreddiwar, A. (2015, September 29). 8 Risks in the Banking Industry Faced by Every Bank. Retrieved from Medici: https://gomedici.com/8-risks-in-the-banking-industry-faced-by-every-bank/
Q2 Solutions
Solve i using Formula
i = (1 + )n -1
1) 5.52% payable annually
i = (1 + )1 -1
=5.52%
2) 5.50% payable semi annually
i = (1 + )2-1
=5.576%
3) 5.48% payable quarterly
i = (1 + )4 -1
=5.594%
4) 5.45% payable monthly
i = (1 + )12 -1
=5.588%
Answer: 5.52% payable annually provides the lowest cost of finance.
Q3. Solutions
- EMV decision rule
EMV (Fixed deposits) =0.3*5.5% + 0.5*5.5% +0.2*5.5%= 5.5%
EMV (Stock mutual fund) =0.3*12% + 0.5*9% +0.2*-2%= 7.7%
EMV (Bond) =0.3*10% + 0.5*8.7% +0.2*3%= 7.95%
Answer: Select bonds because it has the highest payoff
- EOL (expected opportunity loss)
EOL (Fixed deposits) =0.3*(12%-5.5%) + 0.5*(9%-5.5%) +0.2*(5.5%-5.5%)= 3.70%
EOL (Stock mutual fund) =0.3*(12%-12%) + 0.5*(9%-9%) +0.2*(5.5%-(-2%))= 1.50%
EOL (Bond) =0.3*(12%-10%) + 0.5*(9%-8.7%) +0.2*(5.5%-3%)= 1.25%
Answer: Select stock mutual funds because it has the lowest expected opportunity loss
3.
=Maximum payoff – Expected payoff)*$100,000
Maximum payoff = 0.3*12% + 0.5*9% +0.2*5.5%= 9.20%
Expected Payoff = 7.95%
=(9.20% - 7.95%)*100,000
=1,250
Answer: XYZ company should be willing to pay $1,250
Dividend Growth Model
V = D/(K-g)
=0.32*1.03 +{1.12-1*0.32*1.032)*(1+1.02/0.1)}
=3.72
Q5. Solutions
Formula
C = SN(d1) – Ke-rT N( d2)
d1 =
d2 = d1 – σ
We are given that S = 42, K = 40, σ = , r = 0.03, T = 3/12 = 0.25.
d1 =
=0.357282
d2 = d1 – σ
=0.122762
Therefore value of call option is:-
C = 42N(d1) – 40e-0.03*0.25 N( d2)
=42*0.63956-40* e-0.03*0.25 *0.548852
=5.071
Answer: Value $5.07
Q6: Solutions
K =43, S0= 42, S2u =45, S2d =38, r = 0.04
If S2 = S2u =45, then the call option will be worth c2u =45-43=2
If S2 = S2d =38, then the call option will be worth c2d = 0
V2 = S2u - c2u = 45N -2 , If S2 = S2u =45
S2d - c2d = 38N, If S2 = S2d =38
For the risk-free portfolio that is used to value the stock option, these two values must be equal i.e.
V2 = 45N – 2 = 38 N . Therefore N = 0.2857
Hence ,
V2 = 45*0.2857 -2 = 10.86
38 * 0.2857 = 10.86
When this is discounted to its present value, it must be equal to the value of the portfolio at time t =0
V0 = S0N – C 0 = V2e-r*2/12
C 0 = S0N - V2e-r/12 = (42*0.2857)-(10.86* e-0.04*2/12) = 1.215
The value of call option is 1.215
Hedge Ratio:
Hedge Ratio = f u − f d S 0 − u − S 0 − d = 2 − 0 *42 – 45 − 42- 38 = 0.2857
i.e There is a 28.57% changes in option values when per $1 dollar change in stock price.
Q7: Solutions
Using calculator
|
Statistic |
ABC Stock |
XYZ Stock |
|
Average Returns |
1.34% |
1.39% |
|
Standard deviation |
0.77% |
3.30% |
|
Geometric mean |
1.34% |
1.35% |
|
Sharpe Ratio |
1.74 |
0.41 |
|
VaR (parametric) |
14,230 |
(809,604) |
|
Correlation coefficient |
0.078 |
0.078 |
When selecting a portfolio, investors should look for assets that are less correlated, high risk adjusted performance, both absolute and relative to the market, and good inflation hedging properties. From above statistic, ABC has a higher Sharpe ratio and positive VaR suggesting that the stock have a good risk adjusted performance. Therefore, I would recommend that Mr John to invest more in ABC stock.
Part b- VaR Combined portfolio
portfolio weight of ABC 50%
portfolio weight of XYZ 50%
return on ABC 1.34%
return on XYZ 1.39%
Standard deviation of ABC 0.77%
Standard deviation of XYZ 3.30%
expected return of the portfolio 50%*(1.34% +1.39%)=1.37%
standard deviation of the portfolio 1.69%
VaR = [Expected Weighted Return of the Portfolio - (z-score 95% CI * standard deviation of the portfolio)] * portfolio value
=(1.37%-(1.65*1.69%))*20,000,000
=($285,209.18)
VaR for combined portfolio is lower than the VaR for stock ABC and higher than VaR for stock XYZ.
optimal weights for A and B based on Minimum Risk approach
Wabc =
Wxyz= 1 - Wabc
Q8: Solutions
Part A
Using calculator volatility of ABC is 0.00005937 and XYZ is 0.00108721
ABC
l= 0.96
σn-12 = 0.00005937
U2n-1 = ((52.93-51.80)/51.80)^2 = 0.000476
EVMA : σn2= l σn-12 + (1-l) U2n-1
σn2 = 0.96*0.00005937 + (1-0.96)*0.000476
=0.0000760
XYZ
l= 0.96
σn-12 = 0.00108721
U2n-1 = ((67.35-67.14)/67.14)^2 = 0.0000098
EVMA : σn2= l σn-12 + (1-l) U2n-1
σn2 = 0.96*0.00108721 + (1-0.96)*0.0000098
=0.0010441
Part B
GARCH (1, 1) model
σ 2 t= ω + α *u2t−1 + β ×σ2 t –1
ABC Shares
ω= 0.000003, α=0.04, and β=0.82
g?ABC?= 1 - a- b= 1-0.04-0.82= 0.14
V (ABC) = w/ g= 0.000003/ 0.14= 0.00002143
Volatility = √ 0.00002143 = 0.004629
XYZ Shares
ω= 0.000002, α=0.05, and β=0.82
g?XYZ?= 1 - a- b= 1-0.05-0.82= 0.13
V (XYZ) = w/ g= 0.000002/ 0.13= 0.00001538
Volatility= √ 0.00001538 = 0.003922
Part c
Garch (1,1) can be used to estimate the long run volatility
ABC Shares
ω= 0.000003, α=0.04, and β=0.82
g?ABC?= 1 - a- b= 1-0.04-0.82= 0.14
V (ABC) = w/ g= 0.000003/ 0.14= 0.00002143
Volatility = √ 0.00002143 = 0.004629
XYZ Shares
ω= 0.000002, α=0.05, and β=0.82
g?XYZ?= 1 - a- b= 1-0.05-0.82= 0.13
V (XYZ) = w/ g= 0.000002/ 0.13= 0.00001538
Volatility= √ 0.00001538 = 0.003922
Comment
The long-run average volatility of XYZ shares is less than ABC. Thus XYZ has a lower risk than ABC . Using the risk return relationship, expected returns for ABC are greater than XYZ.
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