• The most simple approach would be peformance i.e. returns, right?!

• But is it sufficient to track only returns?

How do you select funds?

• The reliability of the scheme too is a critical aspect. Reliability is nothing but volatility.

• A scheme giving good returns but is extremely volatile or unreliable may not find favor with a larger number of investors.

• This calls for a measure of performance which takes into account both returns as well as volatility / reliability.

There is something more...

Understanding Sharpe & Sortino Ratios – By Prof. Simply Simple

• Sharpe Ratio expresses the relationship

between performance of a scheme and its

volatility.

• A higher ratio signifies a relatively less

risky scheme.

• Mathematically is can be expressed as:

Sharpe ratio = Average returns /

Volatility (Std. Deviation)

• Thus if the performance is average

while the volatility is very low, the ratio

becomes large.

• If one were to look at cricket for an

example, a player like Rahul Dravid will

have a decent average (let’s say 40)

and a low volatility (lets say 0.5). Hence

his Sharpe Ratio would be 40/0.5 =80.

What does it mean?

• Virendra Sehwag could have a slightly

higher average than Dravid (let’s say 45)

but his volatility, as we all know, is quite

high.

• Either he makes big hundreds or gets out

for a very low score. Let’s presume his

volatility is 0.75. His Sharpe ratio will then

be 45/.75 = 60 (which is lower than the

Sharpe Ratio of Dravid).

On the other hand…

• Despite a higher average, Sehwag’s Sharpe ratio

is lower than that of Dravid.

• This indicates that simply looking at performance

from the average point of view is not enough to

judge a player.

• One needs to take a look at different dimensions

as well.

So what does this suggest?

• It may be wiser to pick up Dravid for the

longer version of the game, say Test Matches

and Sehwag might be a better pick for the

shortest version of the game, say T-20.

• Also, the ratio will become large if either the

numerator increases or the denominator

decreases.

Hence…

The Sharpe Ratio of Tata

Infrastructure Fund is

0.0899 for the period of

three years from 1st June,

’06 to 31st May, ’09, wherein

Risk Free Rate is assumed

at 6%.

• The Sortino ratio is similar to the Sharpe

ratio, except while Sharpe ratio uses

Standard Deviation in the denominator,

Sortino ratio uses downside deviation.

• It is important to note that while standard

deviation does not discriminate between

upward and downward volatility,

downward deviation does so.

So what is the Sortino Ratio?

• Standard deviation can be high in the case

of excessive upward movement of price and

it may result into a lower Sharpe Ratio.

• Sharpe ratio will be low because the high

standard deviation is the denominator.

• Now we may believe that the scheme is

unsuitable and therefore misrepresent the

real picture (since upward movement is

desirable from an investor’s perspective!).

Thus…

• Hence it was necessary to find another ratio

which differentiates harmful volatility from

volatility in general by replacing standard

deviation with downside deviation in the

denominator.

• Thus, the Sortino Ratio was calculated by

subtracting the risk free rate from the return of

the portfolio and then dividing it by the downside

deviation.

• Sortino Ratio = Performance/ Downside

deviation. The Sortino ratio measures the

return to ‘bad’ volatility.

• This ratio allows investors to assess risk in a

better manner than simply looking at excess

returns to total volatility.

• A large Sortino Ratio indicates a low risk of

large losses occurring.

Conceptually speaking…

• To give an example, assume investment A

has a return of +10% in year one and -10%

in year two. Investment B has a 0% return in

year one and a 20% return in year two.

• The total variance in these investments is

the same, i.e. 20%. However, investment B

is obviously more favorable. Why??

• As the Sharpe ratio measures risk using

standard deviation only, it does not

differentiate between positive and negative

volatility.

The Sortino ratio, on the other

hand, measures performance

against the downward

deviation… so it is able to spot

the negative volatility

associated with investment A

immediately and help us

classify investment B as a

more favourable investment!

The Sortino Ratio of Tata

Infrastructure Fund is

12.796 for the period of

three years from 1st June,

’06 to 31st May, ’09,

wherein Risk Free Rate is

assumed at 6%.

To Sum Up

• Sharpe Ratio: Sharpe Ratio expresses the relationship between performance of a scheme and its volatility. A higher ratio signifies a relatively less risky scheme.

• Sortino Ratio: The Sortino Ratio is calculated by subtracting the risk free rate from the return of the portfolio and then dividing it by the downside deviation.

Hope you have now understood the concept ofSharpe & Sortino Ratios

In case of any query, please e-mail professor@tataamc.com