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The Investment: Risk and Return

In any investment, risk and return are most important to consider. From the table below, the risk shown can be diversified away by increasing the number of securities is the specific risk of any stock. The market risk is the risk related to Market-wide factors such as interest rates, inflation, economic activity, exchange rates, and unemployment. Thereby, diversification helps bringing unsystematic risk towards zero so that the investor has to only deal with systematic risk. Thus, analysing the investor’s portfolio we can conclude whether the investor is risk loving, neutral or risk averse. Using excels the annual returns and standard has been calculated and are as shown below;

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NAB BHP FOSTERS LEIGHTON ALL ORDS 10 Year Gov Bonds
Average Annual Returns 12.95% 18.50% 12.41% 23.45% 10.33% -0.18%
Standard Deviation 25.32% 36.78% 29.68% 49.35% 22.93% 20.77%
variance 0.0641097 0.1353012 0.08808597 0.24358149 0.0525947 0.043146727

The theoretical relationship between risk and returns could consider the concept of ‘utility’. Utility is a function of expected return and the risk of that expected return, i.e. E (U) = f [E(R), Risk] (Lecture 4 notes). The returns from investments are normally distributed. The more dispersed or widespread the distribution, the greater the risk involved (Peirson, et. al, 2009). Thus, investors prefer the highest expected return for a given standard deviation and the lowest standard deviation for a given expected return.

The assumption of risk aversion states that variability of an expected return reduces its utility. Therefore, there is a trade-off between risk and return. Given these assumptions, it can be shown that it is rational for a utility-maximising investor to hold a well-diversified portfolio of investments (Peirson, et. al, 2009). There is a direct relation between the annual return and standard deviation, which is a measure of risk. From the table we cannot say that there is no specific relationship between return and risk of some stocks and government bond.

As much of the variability of returns on shares is due to factors that are specific to each company, so when shares of different companies are combined in a portfolio, the effects of the company-specific factors will tend to offset each other. Usually, holding a portfolio of about 25-30 securities will help to remove unsystematic risk (Peison, et. al, 2009). Thus, the risk of a well-diversified portfolio can be measured by the standard deviation of portfolio returns.

As unsystematic risk can be eliminated by diversification, the capital market will not reward investors for bearing this type of risk. The capital market will reward investors for bearing the risk inherent in the market portfolio. The reward for bearing systematic risk is a higher expected return, and according to the CAPM, there is a simple linear relationship between expected return and systematic risk as measured by beta (Peirson, et. al, 2009).

The betas of the companies are as follows

NAB BHP FOSTERS LEIGHTON ALL ORDS 10 Year Gov Bonds
Average Annual Returns 12.95% 18.50% 12.41% 23.45% 10.33% -0.18%
Standard Deviation 25.32% 36.78% 29.68% 49.35% 22.93% 20.77%
variance 0.0641097 0.1353012 0.08808597 0.24358149 0.0525947 0.043146727
covariance with allords 0.0419534 0.0600739 0.04199832 0.043878314 0.0508416 0.009017021
BETA 0.7976724 1.1422032 0.79852743 0.834272271 0.9666667 0.17144348

Beta coefficient tells us the response of the stock’s return to a systematic risk. Beta measures the responsiveness of a security’s return to a specific risk factor, the return on the market portfolio (Ross, et. al., 2010). Any stock with a beta of more than one means that the stock is more sensitive to market fluctuations while that one with less than one is said to be less sensitive to fluctuations in the market forces. In this case, it is clear that any change in the market will little impact on the return of stocks as they have betas of less than one.

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T the correlation of each pair is as shown below;

Step 3: calculate variance-covariance matrix
NAB BHP FOSTERS LEIGHTON ALL ORDS 10 Year Gov Bonds
NAB 0.0619727
BHP 0.0316707 0.1307912
FOSTERS 0.0407145 0.0253617 0.08514977
LEIGHTON 0.0387316 0.057759 0.01873042 0.235462107
ALL ORDS 0.0419534 0.0600739 0.04199832 0.043878314 0.0508416
10 Year Gov Bonds -0.0035669 0.025508 0.00199854 0.043878314 0.0508416 0.041708502
correlalation covariance of xy
stdxXstd dev y
NAB BHP FOSTERS LEIGHTON ALL ORDS 10 Year Gov Bonds
NAB 0.966667
BHP 0.340052 0.966667
FOSTERS 0.541793 0.232313 0.966667
LEIGHTON 0.309943 0.318161 0.127871 0.966667
ALL ORDS 0.722493 0.000003 0.617032 0.387665 0.966667
10 Year Gov Bonds -0.067820 0.064496 0.032418 0.428010 0.000302 0.966667

Correlation measures a linear relationship between two stocks. From the calculations above there is positive correlation between the stocks but they have a negative relationship with 10 year government bonds.

The correlation between the two variables will be zero if they are not at all related to each other. In a number of situations, returns of any two securities may be weakly correlated. If an investor invests his money in negative correlated stocks she can reduce the risk instead in investing in one.

Positive correlation between assets in the market tends to bring the variance higher and vice versa. No matter how good the portfolios business prospects of any company are or the quality of the management of that business is, the stock prices are always depressed with the situation in the general market. The stock prices and portfolios of most of the companies are always in a close correlation with the general market trend.

To depict the possible correlation in variances of stocks is set on a basic assumption that the there is serial correlation in the variances. All other indications of correlations between the amounts of use of other combinations were largely positive. These investors to go against the prevailing wisdom of other investors and against the market demands. They, however, possess unyielding confidence that sustains them against market trends. Momentum traders, on the other hand, were found to be the least risk averse. They tend to believe in miscalculations of the less experienced for which opportunity they seize to invest. They also rely more on technical analysis and are thus aggressive market pursuers.

Capital Asset Pricing Model (CAPM)

CAPM is one of the models in valuing assets under uncertainty. It is a model which links expected return to a single source of risk. CAPM proposes that there is a linear relationship between the expected rate of return on an asset and its risk as measured by its beta factor (Peirson, et al., 2009). Under the CAPM model, the expected return demanded by investors on a risky asset depends on the risk-free rate of interest, the expected return on the market portfolio, the variance of the return on the market portfolio, and the covariance of the return on the risky asset with the return on the market portfolio (Peison, et, al. 2009).

The risk-free interest rate – the assets closest to being risk-free are government debt securities, so interest rates on these securities are normally used as a measure of the risk-free rate.

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Rs = Rf + Bs (Rm – Rf)

Where: Rs = the return required on the investment, Rf = the return that can be earned on a risk-free investment index –government bonds, Rm = the average return on all securities and Bs = the security beta (systematic) risk

Using the information on the table above, expected return for each of the four stocks will be

NAB BHP FOSTERS LEIGHTON ALL ORDS 10 Year Gov Bonds
BETA 0.7976724 1.1422032 0.79852743 0.834272271 0.9666667 0.17144348

Rf = -0.18%

Rm = 10.33%

NAB

Rs = -0.18% + 0.798 (10.33% +0.18%) = 8.21%

Expected return = 8.21%

BHP

Rs = -0.18% + 1.14 (10.33% +0.18%) = 11.80%

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Expected return = 11.80%

Fosters

Rs = -0.18% + 0.799 (10.33% +0.18%) = 8.22%

Expected return = 8.22%

Leighton

Rs = -0.18% + 0.834(10.33% +0.18%) = 8.59%

Expected return = 8.59%

The expected return of the stocks with higher betas was high as compared to those with low return.

Creation of portfolio

NAB BHP FOSTERS LEIGHTON Portfolio Expected
Average Annual Returns 12.95% 18.50% 12.41% 23.45%
Standard Deviation 25.32% 36.78% 29.68% 49.35%
BETA 0.7976724 1.1422032 0.79852743 0.834272271
Proportion 0.27 0.22 0.24 0.27 1
Average Annual Returns 3.4965% 4.07% 2.9784% 6.3315% 16.88%
Standard Deviation 6.8364% 8.0916% 7.1232% 13.3245% 35.38%

The proportion taken aims at reducing risk of the profits fluctuating by large margin. Form analysis we show that correlation is an important determinant of portfolio risk. To further pursue this issue, we need to know how to calculate portfolio variances directly.

There is a term involving the squared weight and the variance of the return for each of the three assets as well as a cross term for each pair of the three assets. The cross- term involves pairs of weights, pairs of standard deviations of returns for each asset, and the correlation between the returns of the asset pair.

Reference List

Peirson, G., Brown, R., Easton, S., Howard, P. & Pinder, S. (2009). Business Finance. Sydney: Mc-Graw Hill.

Ross, S.A., Westerfield, R.W. & Jaffe, J. (2010). Corporate Finance. New Delhi: Mc-Graw-Hill.

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