Excerpt

## Table of Contents

Introduction:

Executive Summary:

Return and risk characteristics of ProIndex fund

Risk and return features of ProValue fund and compare with S&P 400

Different level of investment in the ProValue fund:

Active Vs Passive Investment

Active investment

The benefits of active investment

The drawbacks of Active Investment

Passive Investment:

The benefits of passive investment

The drawbacks of Passive Investment

Appendix:1

Appendix:2

Appendix:3

Appendix:4

Appendix:5

Appendix:6

Appendix:7

Appendix:8

Referrences:

## Introduction:

It is very important for a company to identify the associate risks, understand the causes of risks and find out the way to minimize the risks and how these can affect the required return by investors in order to achieve its objectives.

The objective of this report is to consider and calculate the return and risks characteristics of the two investment funds managed by Thompson Asset Management. Information through standard deviation, correlation, beta calculation, Sharp ratio, Treynor ratio Jensen's Alpha, Tracking Error and Information Ratio have been obtained to prepare the report.

## Executive Summary:

- Even though ProIndex fund has higher standard deviation than the benchmark but its associated risk may be compensated as it has achieved three times more return than the benchmark. Other performance measures also demonstrate that ProIndex is less risky.

- Even though ProValue fund has higher standard deviation than the benchmark S&P 400 but its associated risk may also be compensated as other performance measures demonstrate that ProValue is less risky.

- A portfolio of 10 stocks where each of them equally weighted with 10% of the portfolio. The desired return is 26.1% which is moderately higher than the maximized portfolio.

- Choosing between active and passive investment depends on the risk attitude of an investor. If an investor wants grater return and high exposure to uncertainty, they can follow active investment strategy but if anyone wants to have less exposure to uncertainty passive investment will be appropriate for them.

## Return and risk characteristics of ProIndex fund

In order to evaluate the return and risk feature of ProIndex fund, firstly we need to find out the return of ProIndex fund together with the return of the benchmark S&P 500. We can calculate these two by utilizing the entire set of data in the case exhibit 1. Appendix 1 accommodates the calculation by utilizing the following formula to find out the daily holding period return (HPR).

HPR= (End value / beginning value) - 1

Appendix 1 Colum C, D, and E contain the return of ProIndex, return of S&P 500 and difference between two accordingly. The difference between two can be utilized to identify comparative performance measure.

Appendix 2 contains the calculation of relevant risk measure which is very straightforward. Normal statistical computation for standard deviation has been used to calculate daily standard deviation with utilizing the Excel= Stdev () formula. The result of daily standard deviation has been multiplied by square root of 252 which is the number of trading days in a year after deducting bank holidays. (Bodie, Kane, and Marcus, 2011)

From the case exhibit 2 we can see that ProIndex has made 303.06% return during 2009 to 2013 whereas S&P 500 achieved 104.63% over this period. Therefore, the supplementary risks seem to be sufficiently compensated even annual standard deviation for ProIndex fund about 11% which is higher than S&P 500 whereas 30.32% for ProIndex and 19.47% for S&P 500.

Now it seems to me appropriate to identify the correlation between ProIndex and S&P 500 return which represent the return of one relates to the return of other. Excel= Correl () formula has been used in order to identify the correlation between two. Form the appendix 2 we can see the correlation between two is 0.651.

We can now find out the portfolio’s beta which is a measure of systematic risk of share compared to the systematic risk of the market. Portfolio’s beta can be calculated by using the following formula.

β = cov (ProIndex, Market)/ Market variance

= (σ Index, σ market, market)/ σ2 market

By using the correlation of 0.651 I have found the portfolio beta of 1.014 (appendix 2). However, ProIndex has been performing well and less risky than market as it has produced holding period return 303.06% which is almost three times higher than S&P 500 as their holding period return is 104.63% over the last 5 years. (Appendix 1)

To evaluate the performance of the company we can calculate Sharp ratio (SR) which is usually used to identify portfolio’s excess return per unit of risk, on the other hand for diversified portfolio we need to use Treynor Measure (TR).

SR= (Portfolio return- Risk-free rate)/ Standard deviation of portfolio return

TR= (Portfolio return- Risk-free rate)/ Portfolio beta

In appendix 2 we can see that Sharp Ratio is 1.007 and Treynor Measure is 0.301. Both of the ratios demonstrate that the company is able to provide risk adjusted return more than appropriate benchmark. (Bodie, Kane, and Marcus, 2011)

It seems to me appropriate to calculate Jensen’s Alpha (JA) which is used to calculate portfolio’s return over the required return. Jensen’s Alpha is calculated based on (CAPM) capital asset pricing model.

JA= (Portfolio return- Risk-free rate) - βp(Market return- risk-free rate)

From appendix 2, I have found Jensen’s Alpha is 16.1% which indicate the company is less risky than the market. (Bodie, Kane, and Marcus, 2011)

Moreover, I have found Daily Tracking Error 1.45% Annualized Tracking Error 23.01% Information Ratio 0.7082 accordingly (appendix 2). All of these indicate that ProIndex is less risky than the market.

## Risk and return features of ProValue fund and compare with S&P 400

In order to evaluate the risk and return feature of ProValue fund firstly we need to find out the return of ProValue fund together with the return of the benchmark S&P 400. We can calculate these two by utilizing the entire set of data in the case exhibit 6. Calculation of each stock is in appendix 3 and the calculation for the whole portfolio is in appendix 4 which have been done by following formula to find out the daily holding period return (HPR).

HPR= (End value / beginning value) - 1

In appendix 4 Colum C, D and E contain the return of ProValue, return of S&P 400 and difference between two accordingly. The difference between these two can be utilized to identify comparative performance measures.

We need to calculate the return correctly for each quarter’s last day because at the last days the company bought extra securities and included more funds. Before the calculation of the return the addition must be deducted from the ending value. For instance, the original return on 30 September 2013 is -0.344% where the fund was $6051789 at the start and $1006632 was included at the end of the day to the portfolio which was for buying 26,400 LPLA’s share. Therefore, the total fund should be $7037626. However, 16.29% return will be appeared for the day if the calculation done incorrectly.

Appendix 5 contains the calculation of relevant risk measure which is very straightforward. Normal statistical computation for standard deviation has been used to calculate daily standard deviation with utilizing the Excel= Stdev () formula. The result of daily standard deviation has been multiplied by square root of 252 which is the number of trading days in a year after deducting bank holidays. (Bodie, Kane, and Marcus, 2011)

Annual standard deviation for the ProValue fund is 16.76% which is higher than S&P 400 benchmark’s 13.2% which may indicate that the risk associated with the ProValue fund is higher than the benchmark.

The correlation between ProValue and S&P 400 is 0.814 (appendix 5) which means that these two are related but there are other influences on the relationship between two. Normal Excel= Correl() formula has been used for the calculation. (Collins and Fabozzi, 1999)

We can now find out portfolio’s beta which is a measure of systematic risk. Beta can be calculated by using following formula.

β = cov (ProValue, Market)/ Market variance

= (σ Provalue, σ market, market)/ σ2 market

The portfolio beta is 1.034 (appendix 5) which is greater than 1. Therefore, the security’s price will be volatile with the market.

To evaluate the performance, we can calculate Sharp Ratio (SR) which is used to identify portfolio’s excess return per unit of risk, on the other hand for the whole portfolio we can use Treynor Ratio (TR).

SR= (Portfolio return- Risk-free rate)/ Standard deviation of portfolio return

TR= (Portfolio return- Risk-free rate)/ Portfolio beta

From appendix 5 we can see that Sharp Ratio is 3.001 and Treynor ratio is 0.487 where both of them higher compared with ProIndex and S&P 500. Higher the Sharp Ratio and Treynor ratio is better. Therefore, the company is able to provide risk adjusted return more than the adjusted benchmark (Bodie, Kane, and Marcus, 2011).

It is appropriate to calculate Jensen’s Alpha (JA) which is measure whether the additional return is adequately compensates the additional risks taken.

JA= (Portfolio return- Risk-free rate) - βp(Market return- risk-free rate)

From appendix 5 we can see that Jensen’s Alpha is 23.1% where higher the Jensen’s Alpha is better. Therefore, the company is less risky than the market (Bodie, Kane, and Marcus, 2011).

Another common performance measure is Information Ratio (IR) that compares the company’s Alpha by the nonsystematic risks of the portfolio.

IR= (Return on portfolio- Return on benchmark)/ Tracking Error

Tracking Error (TR) represents the distinction between the benchmark and a portfolio’s return.

Abbildung in dieser Leseprobe nicht enthalten

Where

RP= return on portfolio

RB= Return on benchmark

N= number of return periods.

From appendix 5 we can see that the annual tracking error is 9.74% and Information ratio is 2.4617. Grinold and khan, 1995 stated that information ratio of 1 as exceptional, 0.75 is very good and 0.50 as good. Therefore, the information ratio of ProValue fund is exceptional (Grinold and Khan, 1995). Therefore, information ratio also indicates that the associated risks with the ProValue are compensated.

## Different level of investment in the ProValue fund:

Exhibit 8 contains the historical statistics and current weights for all 11 stocks including 2 new stocks ATO and CNO. The portfolio has 25.67% current expected return by utilizing the weights together with the company’s return in the exhibit 10. We can find the maximized weights of a portfolio together with expected return are 25% and 27%. This information can be found in the case exhibit10 column H and I accordingly.

From the exhibit 10 we can see that the maximize portfolio together with expected return of 25.67% that has annual standard deviation between 13.79% where maximized standard deviation at an expected return of 25% and 15.72% where maximized standard deviation at an expected return of 27%. Currently Standard deviation for 5 years is about 16% (appendix 5) where current portfolio has likely higher standard deviation.

In appendix 6 the variance has been calculated by using matrix algebra together with the 10 stock weights and the variance- covariance matrix. In the same appendix cell C91 an example of the computation of the portfolio variance can be found.

In appendix 6 first three boxes rows 1-2, 5-15, and 18-29 shows the inputs of the optimized portfolio expected return, portfolio correlation and stand-alone stock standard deviation.

Appendix 7 contain a sample portfolio with an expected return close to the current portfolio optimized utilizing the Excel built-in Solver. The Solver tool was to optimize the portfolio variance cell C7 based on weights it chooses in the cell C4 through M4. Solver was set with the following constraints.

- Weight cell C4 through M4 had to added to 100%

- Weight had to be non-negative

- Desired ER cell C6 was between 25.0% and 25.9%

We can see from appendix 7 that the maximized weights for a portfolio with a similar expected return to the current portfolio. Variance-covariance matrix in appendix 6 has been used to calculate the variance. Fully optimized portfolio was better than the portfolio having a higher variance. But there is a weight of Zero for many stocks.

Appendix 8 contains a portfolio of 10 stocks where each of them equally weighted with 10% of the portfolio. The desired return is 26.1% which is moderately higher than the maximized portfolio in the appendix 7. The standard deviation is 27.4% which is higher than optimized portfolio with non-negative weights that has 19.3%

## Active Vs Passive Investment

The debate over the shortcoming and merits of active and passive investment has been started for several decades and it is ongoing. However, both of the strategies have both advantages and drawbacks.

**[...]**

- Quote paper
- Md Kamrul Islam (Author), 2015, Portfolio Management. Return and risk evaluation, Munich, GRIN Verlag, https://www.grin.com/document/461501

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