Performance Indicators

In the analysis of performance of Danish and Turkish mutual funds, four methods have been formulated. Those are Sharpe ratio, Treynor ratio, Modigliani & Modigliani measure and Jensen’s alpha single factor model.

Sharpe ratio is used to evaluate performance of the portfolio by dividing excess return, which is average return of the portfolio minus risk-free rate of return, with the standard deviation of the portfolio. In standard deviation, systematic and unsystematic risks are involved. By doing this, a portfolio has been considered totally in terms of risk. In other words, Sharpe ratio investigates non-normal (excess) returns and total risk of the portfolio.

In this study, Sharpe ratios of both Danish and Turkish mutual funds have different characteristics.

In order to see the progress of the performances of Danish and Turkish mutual funds, 1 year, 3 years and 5 years period average Sharpe ratios have been calculated. The aim is to see how mutual funds react to a unit of risk in short, middle and long time periods. Sharpe ratio is the mostly used technique for performance evaluation of a portfolio. Therefore, the other technique such as Treynor ratio is treated as alternatives to Sharpe ratio. Positive Sharpe ratio means there is an excess return in a given period of time and the money market of the country.

As seen in table 5, in short period of time like 1 year, Turkish mutual funds give better performance when it is compared to Danish correspondents. Turkish mutual funds have an average of 2.14 and Danish mutual funds have -1.33. This means that Turkish funds covers better amount of return as performance for given unit of risk than Danish funds. In addition, the latter has negative Sharpe ratios while in general there is an expectation of good performance from a portfolio in short time period. Table 6 above indicates how many mutual funds in each country have positive or negative Sharpe ratios. Because the numbers mutual funds in Denmark and Turkey are 60 and 60, respectively, giving the amount of positive and negative Sharpe ratios is better explanatory. In

1-year time horizon, 39 Danish mutual funds out of 60 and 51 Turkish mutual funds out of 65 have positive Sharpe ratios. The noteworthy point is although the majority of Danish mutual funds have positive Sharpe ratios, the average of all has a negative value. It is because some of Danish mutual funds such as mutual fund #20 and mutual fund #25 have extremely negative Sharpe ratios (See Appendix 8).

In middle period of time (3 years), mutual funds in both countries have negative Sharpe ratios. The reason is that the fluctuations in the economy and volatility in money markets have negative effects on investment vehicles. In Sharpe ratio, because denominator is standard deviation of the portfolio which is a positive number, the nominator is crucial. Negative Sharpe ratio means negative nominator which is average return of the portfolio is smaller than given benchmark which is the risk-free rate which is central government debt rates of Denmark for Danish mutual funds and Turkey for Turkish mutual funds. 3 years Sharpe ratios for Danish and Turkish mutual funds are -6.50 and -1.24, respectively. As the ratios in 1 year time period, Danish mutual funds have smaller values than Turkish ones. However, there is a reality. Negative Sharpe ratio is a bad signal for investors. Because instead of making an investment like investing in mutual funds with negative Sharpe ratios, an investor should stay in an asset with risk-free rate of return.

As a long-term analysis, Sharpe ratio of 5 years period of time has been calculated. Its importance is because if a mutual fund performs well in long-term horizon, it is a sign of consistency in performance and can be attributed to smart investment decisions of management in economic fluctuations.

Sharpe ratio of Danish mutual funds in 5 years period of time is -6.52 while it is -6.50 in 3 years period of time. The main reason is the economic stability and non-fluctuated money market environment of Danish economy. Its currency of Danish krone is binded to Euro and the low rate of inflation prevents the fluctuations. Still, the problem is very low Sharpe ratio. Sharpe ratio also considers upward price movement as it considers downward price movements. Therefore, it is not easy to say why Sharpe ratios of Danish mutual funds are extremely negative. However, an interpretation can be for a unit of return, Danish investors take high risk.

On the other hand, Turkish mutual funds have relatively lower Sharpe ratio of 5 years time period.

years time span. 5 years time period includes the data between 2006 and 2010. 3 years returns are in between the years of 2008 and 2010. The weight of global economic crisis in sub-prime mortgage crisis in 2008 is higher in 3 years time period. Therefore, bad performances of mutual funds affect Sharpe ratio heavily. The difference of 5 years Sharpe ratios of Turkish mutual funds than Danish mutual funds is the growth rate of Turkish economy in years of 2006 and 2007 which are 6.9% and 4.7%, respectively while it was -6.2% in fourth quarter of year 2008 in domestic product purchaser price¹⁸.

Next, Treynor ratio has been calculated for each mutual funds in Danish and Turkish mutual funds.

Treynor ratio is derived from Sharpe ratio. Its only difference is as denominator, systematic risk is included instead of total risk. Treynor (1965) argues that only systematic (non-diversified) risk generates excess return to a portfolio. Therefore, only systematic risk should be in the denominator of the ratio.

As seen in appendix 8, Treynor ratios are in 3 periods of time, 1-year, 3-years and 5-years. In short term (1 year), 43 Danish mutual funds out of 60 and 29 Turkish mutual funds out of 65 have positive Treynor ratios (look at Table 8). When these results compared to Sharpe ratios in 1- year time period, more Danish mutual funds have positive ratios while it is exactly the opposite in Turkish funds. These can be interpreted as in short term (1 year), excluded unsystematic risk in Treynor ratio which is caused because of the management’s actions and decisions have positive affect for Turkish funds while it is relatively negative in Danish correspondents. In other words, managers’ interventions to the investment decisions in Turkish mutual funds are heavily done and make mutual funds perform better.

In mid-term (3 years), 7 Danish mutual funds out of 60 and 18 Turkish mutual funds out of 65 have positive Treynor ratios. These are more positive results than Sharpe ratios in 3- years. It means that taking only account to systematic risk which happens because of general dynamics of money market gives better performances.

18Economic Indicators 2009, Turkish Statistical Institute, 2009, page 1, 1-132 pages

Although Danish and Turkish mutual funds perform better in 3- years Treynor ratios, this fact is not the same in the long period of 5 years. It is expectable that the longer the period, the worse performances mutual funds show. However, none of Danish mutual funds have positive Treynor ratios in 5-years time while it is only 4 out of 65 in Turkish mutual funds.

In Modigliani & Modigliani measure, the purpose is measuring a portfolios performance with an

“unmanaged” portfolio usually a benchmark instead of ranking like in Sharpe ratio and Treynor ratio (Modigliani & Modigliani, 1997).

The definition of risk-adjustment is because all portfolios’ (mutual funds in our case) risks are equalized to the same level to their relative benchmarks. In the nominator of M² measure, the difference of Sharpe ratio of a mutual fund and Sharpe ratio of its relative benchmark, market index, is taken. By doing so, the risk-adjusted excess return of the portfolio has been taken. Then it is multiplied with the standard deviation of the market index.

Utilized benchmarks in Modigliani & Modigliani measure are as the followings:

• Denmark: OMXC (Copenhagen Stock Market Index for all shares)

• Turkey: ISE National 100 (Main Index of Istanbul Stock Exchange).

There are interesting results in Table 9 and Table 10. Unlike different performances of Danish and Turkish mutual funds in ranking techniques of Sharpe Ratio and Treynor ratio, use of unmanaged portfolios as benchmarks give similar results for both of them.

Table 9 indicates that the average Modigliani & Modigliani measure in Danish mutual funds in 1 year, 3 years and 5 years time horizons are 0.05%, -0.02%, -0,2% while they are 0.04%, -0.02%

and -0.01% in Turkish mutual funds, respectively. The results are dramatic. In 1-year period, average M² measures are positive which means without any interventions of managements of mutual funds, investing into mutual funds in 1 year period can be a good decision. On the contrary, staying in risk-free rate of return level instead of investing in mutual funds seems logical. However, these results are the averages of 60 Danish mutual funds in Danish money market and 65 Turkish mutual funds in Turkish money market.

There is a need for looking at M² measures individually in both markets. The criterion is whether a mutual fund has positive or negative M². Table 10 gives a clear picture of the situation as the following:

Table 10 Number of Funds with Negative and Positive M² Measures in Denmark and Turkey in 3 Periods of Time

*60 Danish Mutual Funds and 65 Turkish Mutual Funds, Source: Own Work

In Table 10, the most crucial point is although the averages of M² measures for both countries’

mutual funds are negative, number of mutual funds that have positive M² are 22 and 28 mutual funds out of 60 in Danish mutual funds while they are 17 and 24 mutual funds out of 65 in Turkish mutual funds with 3- years and 5-years periods of time, respectively. The performances of Danish mutual funds in terms of M² measures are narrowly better than Turkish ones when positive and negative measures are compared.

Jensen’s alpha model is based on capital asset pricing model, the aim is to find the exact performance of a mutual fund instead of calculating the relative performance (Jensen, 1968).

Previous performance measures indicators are based on comparisons, Sharpe and Treynor ratios are ranking-based and M² measure is based on risk-adjustment to the benchmark or market index.

Historical excess returns of mutual funds have been utilized in the analysis with the help of Eviews.

The most important point is an alpha value found in the analysis is the main indicators for the performances of the managements of mutual funds. Significantly positive alphas indicate a superior skill of management of portfolio and significantly negative results are indicators of weak performances of the management of portfolio. The alphas which are significantly not different than zero, the performance is equal to market, index. In other words, management of portfolio has no noticeable impact on the performance of a mutual fund.

Because there is a null hypothesis which tests whether the managements’ decisions affect the performance of mutual funds or not, significance level of 5% is used for total (5-years) period of time. In Turkish mutual funds, in 17 mutual funds out of 65, the null hypothesis has been rejected.

It means that only17 Turkish mutual funds in sample size have been affected by the decisions of managers. On the other hand, in 33 Danish mutual funds out of 60 the null hypothesis has been rejected. In the majority of Danish mutual funds, management of a fund affects the performance (See Table 11).

Another aspect in Jensen’s Alpha is whether management affects positively or negatively the performance of a mutual fund. The sign of the alpha value is the main indicator as mentioned above. Table 12 shows 54 Danish mutual funds and 63 Turkish mutual funds have positive alpha values. It can be interpreted as if the managements’ decisions significantly affect the performances of mutual funds, these would be a positive effect. In appendix 3, the 5 years alpha values of each mutual fund can be seen in detail with 95% confidence level.