Table of Contents

## Sharpe’s Measure

Sharpe ratio measures the excess return relative to total risk (standard deviation). A higher asset’s Sharpe ratio implies that it has better risk adjusted performance. The Sharpe ratio is appropriate for the assets with large amounts of unsystematic risk. Table 3 demonstrates the ranking by Sharpe ratio for the four securities, NZX50 and a managed portfolio which consists of the four securities. All the Sharpe ratios are negative value in the Table 3, which means the T bill bond performed better than these securities during the holding period. However, as the stock market has been underperforming during the observation period, this whole market downturn might be due to a seasonality reason. The Sharpe ratio for the NZX50 has the lowest value which indicates that we still outperformed NZX50 on a risk adjusted basis.

## Treynor’s Measure

Treynor ratio is used to represent the relationship between the excess return over the risk-free rate and systematic risk (beta). The greater is value of the Treynor ratio, the higher return on each of the market risks. Generally, this measurement is useful for the completely diversified portfolios. As shown in Table 4, similar to in Sharpe’s measure, all the values are negative. Obviously, the Treynor ratio of our portfolio is slightly higher than the value of NZX50. Again, it implies that the managed portfolio performed better than market index, regardless of a risk adjusted basis.

## Jensen’s Measure

Jensen’s Alpha is based on capital asset pricing model (CAPM), it measures the return on actual security or portfolio in relation to the expected market return. The positive value of Jensen’s Alpha, it indicates that excess returns of the security or portfolio are compensated for the risk. Based on Table 5, Jensen’s Alpha shows that the managed portfolio earned an excess return which is 0.32% higher than the return implied by the Security Market Line (SML), reflecting the managed portfolio outperformed NZX50. However, Jensen’s Alpha is not appropriate to compare fully diversified portfolios with different betas, and therefore we have looked into more measurements.

## Appraisal Ratio

The Appraisal ratio is also known as the information ratio, it is used to measure how the alpha relates to the unsystematic risk, in the other word, it reflects the ability of a fund manager to pick the security or portfolio that differs from that of the benchmark. The higher the Appraisal Ratio refers to the fund manager has better performance to generate a portfolio. From Table 6, the Appraisal ratio of the managed portfolio is the highest than the four securities and the benchmark. MCY and MFT both have negative value (-0.0275 and-0.0775), however, RBD and FPH have positive value which are 0.0421 and 0.0403 respectively. All in all, based on the Appraisal ratio, the managed portfolio outperformed NZX50.

## M2 Measure and T2 Measure

The M2 measure is also called the Modigliani risk adjusted performance measure, it measures the risk-adjusted return of portfolio. It is similar to the Sharpe ratio, but M2 has an advantage in units of percentage return which is easier to interpret in case of negative returns. The greater M2 ratio is, the better performance of portfolio becomes.

T2 measure is derived from the Treynor measure, it measures the differential between the return on the adjusted portfolio and the return on the market portfolio, which the rationale is the same as the M2. As shown in Table 7, since the ratio of our portfolio is greater than benchmark, the managed portfolio outperformed NZX50.

Generally speaking, all above risk-adjusted performance methods show that the portfolio has higher values compare with benchmark. According to the above evidences, we consider the managed portfolio outperformed the market index during 11 Dec, 2017 and 19 Jan, 2018.