- CASE PROBLEM
National Financial Advisors (NFA) served a diverse set of clients, some of whom were quite sophisticated, financially, and others who were just starting to invest. The company had been founded almost ten years ago after Dr Michael Ntalianis and his college roommate had set up shop in a two-bedroom storefront. The roommate had soon decided that the financial services industry was not tangible for his tastes, but Dr Ntalianis had found plenty of bright young minds to come aboard in the meantime. As the firm grew, Dr Ntalianis developed a reputation for training his associates and helping them establish themselves in the business. Dr Ntalianis’ personal reputation for honesty and fair dealing benefited the firm’s reputation, and NFA had built a large customer base during its short life.
THE SENIOR TEAM
Most employees had become used to long hours at work and the extra reading and assignments that Dr Ntalianis constantly asked them to work on. They all realized that they still had a lot to learn about financial services, and finance in general, and they all looked forward to each assignment.
Recently, Dr Ntalianis had asked several senior employees (Senior Team) to develop a presentation and a set of educational materials regarding the different types of risks that investors might face when placing their money with the firm. Some of the information that they had collected for this assignment was rather rudimentary, but the difficulty of the task came in explaining things clearly to investors.
The team’s assignment had come about when one of Dr Ntalianis’ longtime associates had relayed a question from a client: what is this whole risk thing, anyway? There was no simple way to answer this question, unfortunately, but Dr Ntalianis had asked his team to break it down into its simplest components and figure out a way to show clients how risk was treated in the financial markets and when making investment decisions. The presentation could be as basic or as complex as the team felt was necessary.
According to Dr Ntalianis, there were two ways to understand how risk could be measured in conjunction with an investor’s portfolio, or risk could be measured, in a traditional sense, as the chance of loss on some project or single investment. He had stressed that the team would have to work out these two different meanings of risk in the presentation and make sense of each. In addition, Dr Ntalianis was concerned that the techniques used in finance appeared to be complicated and tedious, and he wanted this presentation to point out an example of each concept discussed and demonstrate how the techniques actually made sense when considered carefully. It was Dr Ntalianis’ belief that even the most sophisticated clients could benefit from a good example now and then.
BY THE NUMBERS
Dr Ntalianis had provided several sets of numbers for the team to use in the presentation. The first set was a group of returns for three different stocks, classified by the type of economy that these stocks might face in the future and the return each was likely to experience in the different situations (Exhibit 1). To be conservative, each future scenario was considered to be equally likely. Dr Ntalianis was convinced that there was some way to measure and compare the risks of these potential investments, together and as separate purchases, but he suggested that the team might have to be creative when coming up with such a measure.
In addition to measures of risk for individual stocks and/or projects, Dr Ntalianis wanted the presentation to deal with how investors measured risk when a portfolio was being considered. Dr Ntalianis pulled some representative numbers from the Internet: annualized monthly returns for the market index and two different stocks (Exhibit 2). He indicated to the team that the proper measure of risk for a portfolio would have to be calculated using this kind of data series.
Exhibit 1: Probable returns for several different investments.
Economic situation
Probabilities
Swagman Ltd
Gaslight Ltd
Airspace Ltd
Recession
25%
-2.00%
2.54%
15.46%
No change
25%
6.57%
4.35%
7.50%
Growth
25%
9.21%
6.78%
4.60%
Boom
25%
14.50%
9.71%
1.54%
Historical Correlations
Swagman & Gaslight 0.357
Gaslight & Airspace -0.275
Swagman & Airspace -0.071
Exhibit 2: Annualised Monthly Returns for the Market Index and Two Traded Stocks (Axel & Titan).
Month
Market index (%)
Axel Ltd (%)
Titan Ltd (%)
1
5.08
2.37
1.05
2
5.08
1.37
11.90
3
5.50
1.30
-1.50
4
1.19
7.71
-7.37
5
-1.79
1.14
13.26
6
-1.62
1.51
-0.70
7
-1.13
6.29
6.42
8
5.09
3.88
9.87
9
8.10
8.26
-0.47
10
0.84
0.61
-3.17
11
1.70
0.12
5.12
12
2.74
0.90
-15.58
13
6.03
10.83
18.81
14
5.71
10.31
9.84
15
8.64
35.37
-2.12
16
11.00
22.64
-10.67
17
0.49
7.31
-7.72
18
7.90
2.22
-17.83
19
7.25
10.51
-1.84
20
0.88
3.76
3.44
21
6.17
19.47
-1.31
22
3.67
5.99
2.23
23
2.08
8.93
7.42
24
1.56
10.81
2.10
Exhibit 3
Dividend History: Annual dividends paid for the last 6 years.
Axel Ltd
Titan Ltd
$1.00
$2.00
$1.02
$2.04
$1.04
$2.08
$1.06
$2.10
$1.08
$2.12
$1.10
$2.14
Questions
Dr Ntalianis has instructed the team to specifically answer all of the following questions:
Using the information given in Exhibit 1, determine expected return for each investment for the next period. In addition, find the standard deviation of return for each investment.
Using your answer to 1, above, and assuming that investors can only invest in one of the three alternatives in Exhibit 1, use expected return and standard deviation to determine which alternative would be the most appropriate for a risk-averse investor. Justify your method of selection.
Determine the expected return and standard deviation of a two-asset portfolio comprised of Swagman and Gaslight shares, Swagman and Airspace shares, and Gaslight and Airspace shares. Assume equal weightings of each share within each portfolio.
Determine the expected return and standard deviation of a three-asset portfolio comprised of Swagman, Gaslight and Airspace shares. Assume equal weightings of each share within the portfolio. Why is the computation more complex than a portfolio comprising of only two shares?
Use the numbers in Exhibit 2 to determine the average return, variance and standard deviation for Axel Ltd, Titan Ltd and the market index.
Use the numbers in Exhibit 2 to determine the systematic risk (Beta) of both Axel and Titan Ltd.
Which measure, beta or standard deviation, is more useful when analyzing stocks that are placed in a diversified portfolio? Provide justification for your answer.
Use the capital asset pricing model to calculate the required rate of return for both Axel and Titan Ltd. Assume the risk-free rate of return is 6%. Define what is meant by the required rate of return.
Utilising the required rates of return calculated in question 8 above and the historical dividend information in exhibit 3; calculate the intrinsic value for both Axel and Titan Ltd. List all assumptions that you make to form your valuation.
