## Sharpe ratio, risk, return and alpha

According to Sharpe ratio, risk and return are directly proportional. For every additional risk, there is an additional return. Sharpe ration is normally used to evaluate the adjusted risk of a portfolio, which can only be achieved if risk-free assets such as government Treasury bills and bonds, which are considered less risky, are used as the benchmark.

This is then used to determine the additional risk that a portfolio may come with. Sharpe ratio is driven by three main factors including the rate of return from the portfolio, the risk free rate of return and the portfolios standard deviation. This ratio tells whether high returns are realised because of wise investment or just risk taking. In the above scenario, when alpha doubles, the overall risk of the portfolio is expected to increase.

Alpha is a performance measurement ratio. It looks into the precariousness of a portfolio’s return while drawing comparisons with that of a risk-free asset. Just like standard deviation, alpha has a direct relationship with the returns of an asset. A positive alpha tells or shows an over performance whereas a negative alpha depicts an under performance of an asset. In addition, the beta of this asset is expected to increase since it is a measure of risk.

## Beta, alpha and standard deviation

Beta, alpha, standard deviation, covariance and Sharpe’s ratio are some of the parameters used in risk evaluation. All of them are driven by the return on investment and the amount of risk involved in the investment. Therefore, it is imperative to note that if alpha doubles or varies, the other measures of risk that are dependent on alpha will also vary appropriately.

This indicates that alpha, covariance, standard deviation, beta and Sharpe’s ratio are related and any variance or change in one of them causes the change of the other variable relatively. From the above computation, IVS proves to be more risky with a beta of 1.348, followed by EIB at 1.2672. The latter tells us that EIB is the least risky if beta is to be used to evaluate its performance. Risk premium still shows that IVS is the most risk and the less risky is EIB with a risk premium of 0.04. This therefore tells any potential investor that if risk is his or her basis of decision-making then the most appropriate or convenient investment is EIB, which poses the least risk.

If return on investment is anything to go by as an investment motive then IVS promises the highest return than any other asset in this portfolio. Any investor who considers himself or herself a risk taker is advised to invest in IVS as opposed to any other asset since IVS promises the best reward in terms of returns. Correlation advises that an investor can only invest in two assets at the same time if there is a correlation between these assets. In this case, IVS and EIB have a correlation of 0.08 and 0.7 respectively. This means that they tend to move in a particular direction and it would be appropriate for an investor who would wish to reduce his or her risk of investment.

## Annualized holding period

Holding assets that are perfectly correlated negatively reduces the investment risk. Efficient portfolios provide the highest possible returns. The investor should ensure that he or she holds those assets that will minimise his or her risk. He or she should therefore diversify his risk. In a diversifiable risk, an investor can eliminate risk in an efficient portfolio. The non-diversifiable risks on the other hand are those risks that still exist in well-diversified and efficient portfolios. The investor therefore seeks to eliminate the diversifiable risk.

Capital Asset Pricing Model (CAPM) defines the connection between risk and the required rate of return. It assumes that investors are rational and they choose among alternative portfolios based on each portfolio’s expected return and standard deviation. Investors have similar expectations regarding return to investment. In this case, all assets are marketable and divisible. In other words, it is believed under this model that the capital market is efficient and perfect.

R_{I=}R_{F} + [E (R_{M} – R_{F})] ß

Where R_{ib} is required return of security I

R_{F} is the risk free rate of return

E (R_{M}) is the expected market rate of return

ß = Beta.

Therefore, looking at the case in hand, we calculate the expected return given the prevailing conditions.

Portfolio I

R_{ib} = R_{F} + [E (R_{M} – R_{F})] ß = 8 + [13(13-8)] (25/100)^{2}= 12.06%

The required rate of return for this security is therefore 12.06% and anything that gives below this rate should be rejected. In a real investment, there is no ideal condition, thus investors are forced to hedge or reduce their risks, which is why acquisition of insurance is necessary to guard the investor against losing his or her money, as well as investments. The investment portfolio is doing well. Currently, the portfolio’s performance is outdoing the market average.