# BEO2431 Risk Management Models

Q1 Identify and rank risk factors that are considered in financial institutions and non-banking cooperation.

Q2. XYZ Property development Ltd is offered a choice of loan funds at the following nominal interest rates:

- 5.52% payable annually
- 5.50% payable semi annually
- 5.48% payable quarterly
- 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?

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.

Q3-1. What decision should be made according to the EMV decision rule?

Q3-2. What decision should be made according to the EOL (expected opportunity loss) decision rule?

Q3-3. How much XYZ company should be willing to pay to obtain a market forecast that is 100% accurate.

Q3-4. Draw a decision tree to this problem

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.

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…)

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.

**Covariance Matrix**

RABC | RXYZ | RASX200 | |

RABC | 0.0000442 | ||

RXYZ | 0.0000145 | 0.000815 | |

RASX200 | 0.0000174 | 0.000161 | 0.0000596 |

- Calculate the optimal weights for A and B based on Minimum Risk approach.
- calculate the Systematic Risk (β) for share A and Share B and comment on these values

Q8. Volatility Forecasting

(a) Calculate the volatility (σ^{2}) of ABC and XYZ Shares. The parameter λ in the exponential weighted moving average (EWMA) σn^{2} = λ σ_{n}-1^{2} + (1-λ) U^{2}n-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 (σ^{2}) and EWMA model?

(b) 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

(c) Estimate the long-run average volatility of ABC and XYZ and comment on these values

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