INV4801/201/3/2022
Tutorial Letter 201/3/2022
Investments: Portfolio Management
INV4801
Semester Course
Department of Finance, Risk
Management and Banking
This tutorial letter contains important
information about the Assignment 1.
Bar code
Question 1
[25 marks]
a) Formulate each of the following constraints of Joseph’s investment policy statement (IPS):
i.
liquidity
ii.
time horizon
(2)
(2)
Liquidity Needs for Abigail Joseph:
Joseph will fund education expenses for her children in one year at a cost of $ 50,000. √√Joseph has no other
liquidity needs.
Time Horizon Constraint for Abigail Joseph:
Joseph has a long-term, multi-stage time horizon. √√The first stage is one year until education costs are paid.
The next stage is Joseph’s employment years, 28 years, until her retirement. The last stage begins at her
retirement.
One year later, after prepaying her children’s education costs and after making her annual RA contribution, Joseph has
an equivalent of R 4,000,000 invested in her RA, the mount that was donated by her aunt in South Africa. Joseph’s
other financial information remains the same.
b)
State the return objective portion of Joseph’s IPS.
(5)
Return Objective Statement:
Joseph’s return objective is to grow the investable portfolio to purchase a $ 3,000,000 pretax annuity in 28 years
at age 66. √Since she will receive a pretax payment of $2,000,000 upon retirement from Econet Wireless, the
investment portfolio needs to provide R 1,000,000 of the necessary R 3,000,000. √ Joseph’s expenses are $
96,000. Given the tax rate of 25%, Joseph will need 96,000 / (1 - 0.25) or R 128000 √of pre-tax income to generate
the after-tax income for meeting these expenses. Therefore, Joseph’s current pretax annual compensation of
$140,000 will be able to support a contribution √ of $7,800 and remain with the excess is 140,000 – 128000√ or
$12000. √. Remember this contribution is included in her annual living expenses.
c)
Calculate Joseph’s required average annual pretax nominal rate of return until her retirement in 25 years. Show
your calculations.
(5)
Exchange rate a year later
= 15.24x1.045/1.015
=15.69√
Return Calculation:
Investment Portfolio (pretax)
Current portfolio
R4000000/15.69
($254,939.45-50 000+12000) (college fees and excess) (216 939,45)
Assets Needed to Purchase Annuity at age 65 (pretax)
Required portfolio value
Lump-sum benefit at age 65
Required value of RA
Required Return Calculation
Present Value (PV)
PMT
Future Value (FV)
Number of Years (N)
CPT I/Y – TVM registry of calculator 2.95% pretax nominal√
2
3,000,000
(2,000,000)
1,000,000
(216 939,45)√
(12 000)
1,000,000√
28√
INV4801/101
d) Identify two factors that decrease Joseph’s ability to take risk.
(4)
Factors that decrease Joseph’s ability to take risk:
• Joseph has two children and needs university fees. √√
• Joseph desires to make annual pretax contributions $ 7,800 to a charity. √√
e) Identify two factors that decrease Jasi’s ability to take risk.
(4)
Factors that decrease Jasi’s ability to take risk:
• Jasi’’s living expenses exceed the annual income. √√
• Jasi’ has 4 children and these mighty need university fees in the future √√
• Jasi’s early retirement plan. √√
• Jasi will sell her business and donate the funds. √√
f)
Determine whether Joseph or Jasi has a greater willingness to take risk. Justify your response with one reason.
(3)
Jasi has a greater willingness to take risk because:
• Jasi owns her business. √
• Jasi plans to retire relatively early. √
• Jasi is confident that equities will deliver positive returns. √
Question 2
[25 marks
a) Identify two leading cyclical indicators in Exhibit 1 that support Katemba’s observation regarding the RSA equity
market. Explain how the change in value of each of these indicators supports Katemba’s observation and their effect
on equity market.
(6)
The question should have been phased as follows:
b) Identify two economic indicators in Exhibit 1 that support Katemba’s observation regarding the
RSA equity market. Explain how the change in value of each of these indicators supports
Katemba’s observation and their effect on equity market.
(6)
All students were awarded with extra 6 marks.
There are three leading cyclical indicators in Exhibit 1 that support Katemba’s observation:
•
•
•
Average prime rate√
Labor cost per unit of output, manufacturing√
Consumer price index (inflation rate) for services√
The leading indicators referenced by Katemba focus on business activity and consumer sentiment and activity.
Each indicator shows a decrease save for Consumer price index during the quarter, suggesting that the
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economy is deteriorating. √The deteriorating economy should have a negative effect on equity market returns
as expectations are priced into the market√√
c) Calculate the intrinsic value of the JSE All Share Index using the constant growth dividend discount model of market
valuation and the information provided by Katemba. Show your calculations.
(6)
The dividend discount model formula is defined as follows:
P = D1 / (k-g)
Where:
P = intrinsic value
D0 = current dividend rate
D1 = dividend rate in period 1
g = constant growth rate of dividends
k = the required rate of return for stock market (risk free rate + equity risk premium)
Calculate D1 = D0 * (1+g):
D1 = (777*0.04)*(1+0.07) = 33.26√√
Calculate k-g:
k-g = (0.03+0.10)-(0.07) =0.06√√
DDM:
D1 / (k-g) = 33.26 / 0.06 = 554,33√√
d) Select the two adjacent corner portfolios to be used in finding the most appropriate strategic asset allocation for
Thompson’s investment portfolio.
(2)
Pre-tax required return = ((1+6.5%)(1+1%)-1)/(1-0.25)= 10,09%
Corner portfolios 3 √and 4√ are the corner portfolios to be used in determining the most appropriate
strategic asset allocation for the Thompson Foundation. The portfolio that satisfies Thompson’s return and
risk objectives must lie on the portion of the efficient frontier located between corner portfolio 3 and corner
portfolio 4.
e) Determine the most appropriate allocation between the two adjacent corner portfolios selected in Part (c).
(4)
Using the corner portfolio theorem and the expected returns for corner portfolio 3 and corner portfolio 4, solve
the following equation for w:
10.09 = 10.2w + 9.4(1 – w) √√
The solution yields:
w = 86% and 1 – w = 14% where w represents the weight allocated to corner portfolio 3. Therefore, most
appropriate strategic asset allocation is 86% √in corner portfolio 3 and 14% √in corner portfolio 4.
f)
Determine the percentage that would be invested in long-term RSA Bonds based on the most appropriate strategic
asset allocation found in part (b).
(3)
The percentage invested in long term RSA Bonds given the most appropriate allocation equals the weighted
average of the Intermediate term RSA Bonds allocations in corner portfolios 3 and 4:
Intermediate term RSA Bonds = 0.86 × 0% √+ 0.14 × 36.7% √= 5.14% √
g) Determine, based on the Sharpe ratio criterion, if Ntabeni should include RSA high yield bonds in Zvoushe’s
portfolio. Justify your response with one reason. Show your calculations.
(4)
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INV4801/101
In order to achieve a superior portfolio of risky assets by adding high-yield RSA bonds, the Sharpe ratio for the
high yield bonds must exceed the product of Zvoushe’s existing portfolio and the correlation of the high-yield
bonds with the current portfolio. √Therefore, RSA high yield bonds should not be added because the asset
class Sharpe ratio = (0.057 - 0.023)/0.1033 = 0.3291√ is lower than the Sharpe ratio √of the existing portfolio
multiplied by the correlation between the new asset class and the existing portfolio (0.63 ×0.84) =0.5292. √
= 0.08/(0.1033*(0.85^0.5))=0.84
Prof. Godfrey Marozva, CFA, Ph.D
DEPARTMENT OF FINANCE, RISK MANAGEMENT AND BANKING
©
UNISA 2022
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