Returns are time-weighted. Volatility is the standard deviation of returns. The Sharpe Ratio is calculated by first multiplying the mean monthly returns by a factor of 12 and subtracting the risk-free rate. Subsequently, divide this by the product of the square root of 12 with the standard deviation of the monthly returns to get the Sharpe Ratio. In some years, the risk-free rate used to compute excess returns can be zero or negative. Maximum drawdown is the worst peak to through drop in value in any given year.
MSCIWLRD denotes the MSCI World Index; MSCWRLDUTIL denotes the MSCI WORLD Utilities Index; MSCIWRLDEGY denotes the MSCI WORLD Energy Index; MSCIWRLDIND denotes the MSCI World Industrials Index; MSCIEM denotes the MSCI Emerging Markets Index.
*** means correlation is statistically significant at the 1% confidence level.
*** means the t-statistics is statistically significant at the 1% confidence level.
Market Beta refers to the global market returns, proxied by MSCI World net of the risk free rate; SMB, HML, RMW and CMA refers to the global Fama-French factors (Fama and French, 2012). Subject to Fama French data availability.
Mean-variance spanning tests are used to determine whether adding a listed infrastructure proxy bucket to an existing
investment portfolio significantly increases diversification opportunities. We present below the results of the Kan and Zhou (2012) two-stage test:
The test consists in examining whether the rejection of the Huberman and Kandel (1987) (hereafter H&K) null hypothesis, i.e. whether the efficient frontier is improved when including new assets, is due to differences in the tangency or the global minimum variance as a result of the addition of the listed infrastructure assets.
If the mean-variance efficient frontiers are not statistically different the new asset cannot be said to constitute a new asset class. The p-value indicates the probability with which the null hypothesis of there being no difference cannot be rejected.
Global Fixed Interest proxied by the JP Morgan Global Aggregate Bond Index; Commodities proxied by the S&P Goldman Sachs Commodity Index; Real Estate proxied by the MSCI World Real Estate Index; Hedge Funds proxied by the HFRX Global Hedge Fund Index; OECD and Emerging Market Equities proxied by MSCI World and MSCI Emerging Market Indices, respectively.
*by market value