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Likelihood Inference Sharpe Ratio Asymptotic

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Discuss About The Asymptotic Likelihood Inference For Sharpe Ratio.




The three securities had mixed performances in the 5 year period from 2013 to 2017. Impressively, BHP provided a compound 5 year return of 57% for investors compared to Wesfarmers and NAB which had -37% and -11% respectively. With this, only NAB and BHP beat the market which had a compounded return of -9% over the same period.  NAB had the outstanding performance on average returns of 12% annually compared to Wesfarmers and BHP with an average return of 8.68% and –3.407% respectively.

The volatility of the 5 year period saw NAB have the highest annual return of 40.48% in 2013 compared to BHP’s and Wesfarmers’ maximum return of 27.66% and 21.7% respectively in the same year. On the other hand, BHP suffered the lowest return of -40.45% in 2015 compared to Wesfarmers and NAB -1.295% in 2014 and -2.248% in 2015.


Portfolio Return and Risk

The equal weighted portfolio of the three stocks was not impressive. NAB provided the highest returns but with a high risk while BHP had the lowest return and with the highest risk. The diversified portfolio provided the investor with meagre returns while minimising their exposure to the volatility of the market.

Risk Measure (Sharpe Ratio)

The Sharpe ratio is used to evaluate the performance of a portfolio in totality (Qi, 2016). Wesfarmers had the best Sharpe ratio of the three securities. Thus, it would have delivered investors the highest excess returns at the lowest risk.

Value at Risk (VaR)

VaR is used in measuring the potential loss an asset could suffer on any given day (Bernard et al., 2017). Using a 95% confidence level, Wesfarmers has the least VaR to the 5% worst case scenario. Thus, the investor should focus on Wesfarmers.



Bernard, C., Rüschendorf, L. and Vanduffel, S., 2017. Value?at?risk bounds with variance constraints. Journal of Risk and Insurance, 84(3), pp.923-959.

Qi, J., 2016. Asymptotic Likelihood Inference for Sharpe Ratio.


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