Rating Equity Funds against Return of Random Traders

In this paper, we study the problem of benchmarking returns of equity funds. We present a novel approach, the random-trader scheme, to benchmark return of an equity fund during a specific period. A random trader uses all-in-all-out strategy to trade in the market at random timing with capital being negligible as compared with the market size.In this paper, we study the problem of benchmarking returns of equity funds. We present a novel approach, the random-trader scheme, to benchmark return of an equity fund during a specific period. A random trader uses all-in-all-out strategy to trade in the market at random timing with capital being negligible as compared with the market size. Let DRRT be the distribution of returns of random traders, and R
_rt
be a random variable sampling from DRRT. In this paper we model DRRT as a log-normal distribution, denoted as s
_DRRT
, and provide an efficient algorithm to compute the mean and variance of s
_DRRT
, denoted as μ
_DRRT
and σ
_DRRT
, respectively. Using TAIEX index as data set, our experiments showed s
_DRRT
approximates DRRT well when the length of given period is one month. We then score each equity fund by the cumulative distribution function of s
_DRRT
i.e., s(m; DRRT) = Pr[R
_rt
≤ R(m)] , where R(m) denotes the return of the equity fund m during the given period. Using the historical data on equity funds in Taiwan, we observed interesting characteristics. When analyzing monthly returns, although there are some winners who are able to achieve scores higher than .9 sometimes, it is difficult for them to always keep up at the high scores. However, few equity funds showed the stability of scores higher than .7, when analyzing long-term returns. Furthermore, there are times when most funds obtain high scores. There are also times when no funds perform well.