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In order to evaluate the comparative performance of the robo- advisors and the conventional funds, we employed different measures that have been presented below. The relevance of these methods, in order to gage the funds’ performance measurement, have been well documented in the literature by Christiansen et al. (2020), Coudert and Salakhova (2020), Naqvi et al. (2018), Krishna Reddy et al. (2017).
Adjusted Sharpe Ratio
The Sharpe ratio was introduced by Sharpe (1966), and a refined application of this ratio was presented in Sharpe (1994). This ratio represents the excess return of a portfolio, per unit of the total risk. A higher Sharpe Ratio depicts better performance, whereas a lower Sharpe Ration indicates towards a weaker performance. However, the findings (Lo, 2002), (Israelsen, 2005) and (Lin and Chou, 2003) have raised concerns on the appropriateness of this measure, when it comes to the performance evaluation. The major criticism emanates from the non-normality of the returns, the time dependence and the idiosyncratic returns. Therefore, in order to account for these estimation issues, we use the adjusted Sharpe Ratio of Pezier and White (2006) as follows,
Technological Forecasting & Social Change xxx (xxxx) xxx
study, we have used three different model specifications for Jensen’s alpha. The first one of these is based on the Sharpe (1964) Capital Asset Pricing Model (CAPM). Mathematically, this is expressed as,
Ri — Rf = αi + βi Rm — Rf ) + ui (2)
Where Rf is the risk free rate, and Ri — Rf represents the excess return for the fund i; Rm — Rf is the benchmark excess return, and αiis the Jensen’s alpha.
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In order to establish the robustness of our findings, we employ certain additional asset pricing specifications. In this regard, Fama and French (1992) proposed a three-factor model that accounts for the risk factors that are associated with the firm size, and the book-to-market ratio. This size premium is computed as the difference in the returns between the small caps and the large caps (SMB). Additionally, the value premium is the difference in the returns between the high book-to-market, and the low book-to-market stocks (HML). This can be expressed as,
Ri — Rf = αi + βi Rm — Rf + βsSMBi + βHHMLi + ui (3)
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Moving in the same stride, Carhart (1997) extended this model by introducing a momentum premium (MOM). This has been calculated as the difference between the returns of the past winners and the past losers. We presented the model as,
Ri — Rf = αi + βi Rm — Rf + βsSMBi + βHHMLi + βMMOMi + ui (4)
The momentum factor also takes into account the persistence, as well as the cognitive biases in the investment process, and is also an impor- tant aspect that must be taken into consideration when differentiating the performance of the different funds that are taken into account.
2.4. Data specification
The time period for this research spans over a time period of four years i.e., from January 2016 to December 2019. While data for con- ventional funds are easy available, finding the same for robo advisors is a challenging task. Therefore, the primary selection criteria have chosen
the automated funds that disclose their financial information. Based on
AdSRi = SRi(1 + skew × SRi — ( kurt — 3)) × SR2
(1)
this, we selected 100 robo advisors, based in the United States, for which
6 24 i
the required data was available. To compare the performance with the
Where SRi represent the Sharpe ratio, skew is the skewness, and kurt is the measure for kurtosis.
Reward to value at risk
Assaf (2015), Iglesias (2015), Su (2015) noted that the VAR models are better suited in terms of quantifying the risks, as compared to the standard deviation. Furthermore K. Reddy et al. (2017) provided evi- dence that the VAR based performance evaluation is more appropriate to use, especially when the underlying returns are computed from the NAV. Therefore, for the purpose of computing our sample funds, we estimated the VAR, using a 95% confidence interval. The reward to value at risk is then computed as,
=i
RVAR Ri — Rf
VARi
Where, Ri represents the returns for each fund, and the VARi is the value at risk.
Jensen’s alpha
Jensen’s alpha is a risk adjusted performance metric that has been proposed by Jensen (1968), and captures the excess returns of a fund, as compared to the expected returns. The expected returns are risk adjusted returns, as predicted by a market-based model. For the purpose of this
other funds, we selected an equal number of funds, each of which were from equity, fixed income, money market and the hybrid categories. For these conventional funds, we then considered the largest funds by size. This was undertaken in order to stress test the performance of the robo advisors in comparison with their conventional counterparts. If the robo advisors demonstrate better than big funds, that would eliminate the size constraint. We also included three major indices, in order to consider the performance of passive investment. Moreover, the weekly NAVs have been used to compute the returns for the funds. For the risk free rate, we have used the yield available on 10 year US treasury bonds. Moreover, the SMB, HML premiums have been extracted from the data library pertaining to Kenneth French, while we created the momentum factor using the methodology of Liu and Zhang (2008).
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