Numerical on Sharpe Ratio

[00:00:02]Hey everyone. So now we discuss our numerical on sharp ratio. So here in this numerical we will rank portfolios SNW on the basis of sharp ratio and state whether they have outperformed or underperformed the market index. What we are given in the question is the two portfolios SNW their actual returns 21 and 26 respectively the beta values 1.1 and 1.8 8 respectively and the standard deviation of returns 20 and 25 respectively. We are given a risk-free asset whose actual return is 7% beta 0 because it's risk-free and standard division of reserves returns is again zero. For the market index we have the actual return 19% beta 1 which is again the standard and the standard deviation of returns is 16%. So we begin with our calculations. The formula for the sharp ratio is SPS RP minus RF upon sigma P. So it is the standard deviation of returns. This is our uh risk rate returns and this 21 is our actual returns of actual returns of the portfolio.

[00:01:27]So now uh we create our table.

[00:01:32]We have the portfolio.

[00:01:36]We have RP.

[00:01:38]We have sigma P.

[00:01:42]We have Sharp ratio.

[00:01:48]we have rank and then we'll state whether it has outperformed or underperformed.

[00:01:59]Good. So for portfolio we have S, we have W, we have market index.

[00:02:08]Uh this will be used for comparison with S and W.

[00:02:15]So for S RP is 21 for W it is 26 for mark index it is 19 sigma P values from there 20 25 and 16 right sharp ratio we calculate for using this formula RP is A1 - RF which is 7 all divide by the value 20 which gives us 0.70.

[00:03:02]Next one 26 / 7 wholeide by 25 0.76.

[00:03:10]X9 - 7 / 16 gives us 0.75.

[00:03:18]So now we have to rank it and then state whether it has outperformed or underperformed.

[00:03:27]So this is a market index. We have to rank SNW portfolio.

[00:03:32]We'll rank this portfolio two and one.

[00:03:37]So I'll justify the reason for this one and two ranking. So the portfolio has has underperformed underperformed and why so because it has because it's SP value we have calculated from the sharp ratio value SP is less than from this value for the market index which is SM that's why we have ranked it two why we have ranked it one because it has outperformed. We're comparing SNW.

[00:04:15]So based on that we have given rank one and two. Why? Why it has outperformed?

[00:04:20]Because the SP value which is 0.76 is more than the market value um the sharp ratios market index value which is 0.75.

[00:04:32]So this is the basis for us to uh say whether a particular portfolio has underperformed or outperformed and this is the way how we rank these portfolios.

[00:04:42]Thank you so much.