Financial Analysis: Risk, Valuation, and Portfolio Solutions

This assignment presents solutions to various financial problems. The first section classifies financial and non-financial risks, providing examples for each. The second section calculates effective interest rates for different compounding periods. The third section applies EMV and EOL decision rules to investment choices, and also explores decision tree analysis. The fourth section uses the dividend growth model for stock valuation. The fifth section calculates the value of a call option using the Black-Scholes model. The sixth section uses a binomial option pricing model to value a call option. The seventh section analyzes portfolio risk and return, including Sharpe ratios and VaR calculations, and recommends an investment strategy. The eighth section uses EVMA and GARCH models to estimate volatility. The document provides a comprehensive overview of financial analysis techniques and their applications.

Q1 Solutions
Risks may be classified as financial and non-financial risks (Actuaries, 2018). Examples of
financial risks include:-
1. Credit risk- This is the risk where third parties such as borrowers or counterparty defaults on
their payments.
2. 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.
3. Market Risk- Movements in investment market values, interest rates and inflation rates may
lead to market risk.
4. Business risk- These are specific to the business undertaken as a bank, investing in a business
or project that fails to be successful.
5. 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:-
5. Operational risk – This is an internal risk. It arises from inadequate or failed internal
processes, systems and people.
6. 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 + i(n)
n )n -1
1) 5.52% payable annually
i = (1 + 5.52 % ¿ ¿
1 )1 -1
=5.52%
2) 5.50% payable semi annually
i = (1 + 5.50 %¿ ¿
2)2-1
=5.576%
3) 5.48% payable quarterly
i = (1 + 5.48 % ¿ ¿
4 )4 -1
=5.594%
4) 5.45% payable monthly
i = (1 + 5.45 %¿ ¿
12)12 -1
=5.588%
Answer: 5.52% payable annually provides the lowest cost of finance.

Q3. Solutions
1. 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
2. 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
4 Decision Tree
Q4. Solutions
Dividend Growth Model
V = D/(K-g)
Where D= expected annual dividend next year, k is required return and g is the growth rate
V= 0.32*(1+3%) +{(1+12%)-1*0.32*(1+3%)2*(1+(1+2%)/(12%-2%))}
Fixed Deposit
Stock
Bonds
P=0.2, Poor-5.5%
P=0.3, Good-5.5%
P=0.5, Average-5.5%
P=0.3, Good-12%
P=0.5, Average-9%
P=0.2, Poor--2%
P=0.2, Poor-3%
P=0.5, Average-8.7%
P=0.3, Good-10%
T=0
0.32*1.03
T=2
0.32*1.032*1.02
T=1
0.32*1.032
T=03
0.32*1.032*1.022

=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 = ln ( S
K )+ (r + 1
2 σ 2 )T
σ √ T
d2 = d1 – σ √ T
We are given that S = 42, K = 40, σ = √ 0.22, r = 0.03, T = 3/12 = 0.25.
d1 = ln ( 42
40 ) +( 0.03+ 1
2∗0.22 )∗0.25
√ 0.22∗0.25
=0.357282
d2 = d1 – σ √ T
=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 = [ E ( ra ) −rf ]∗var ( b ) − [ E ( rb ) −rf ] Cov(a , b)
[ E ( ra ) −rf ] var ( b ) + [ E ( rb ) −rf ] var ( a ) − [ E ( ra ) −rf +E ( rb ) −rf ]∗Cov (a , b)
Wxyz= 1 - Wabc
Q8: Solutions
Part A
Using calculator volatility of ABC is 0.00005937 and XYZ is 0.00108721
ABC
= 0.96
σn-12 = 0.00005937
U2n-1 = ((52.93-51.80)/51.80)^2 = 0.000476
EVMA : σn2=  σn-12 + (1-) U2n-1
σn2 = 0.96*0.00005937 + (1-0.96)*0.000476
=0.0000760
XYZ
= 0.96

σn-12 = 0.00108721
U2n-1 = ((67.35-67.14)/67.14)^2 = 0.0000098
EVMA : σn2=  σn-12 + (1-) 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 *u2
t−1 + β ×σ2 t –1
ABC Shares
ω= 0.000003, α=0.04, and β=0.82
 （ ABC （ = 1 -  -  = 1-0.04-0.82= 0.14
V (ABC) =  /  = 0.000003/ 0.14= 0.00002143
Volatility = √ 0.00002143 = 0.004629
XYZ Shares
ω= 0.000002, α=0.05, and β=0.82
 （ XYZ （ = 1 -  -  = 1-0.05-0.82= 0.13
V (XYZ) =  /  = 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
 （ ABC （ = 1 -  -  = 1-0.04-0.82= 0.14
V (ABC) =  /  = 0.000003/ 0.14= 0.00002143
Volatility = √ 0.00002143 = 0.004629
XYZ Shares
ω= 0.000002, α=0.05, and β=0.82
 （ XYZ （ = 1 -  -  = 1-0.05-0.82= 0.13
V (XYZ) =  /  = 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.