Take any asset , Every investor has a specific idea of return as it is based on the expected holding period, ability to short sell, turn over of the asset etc. If one were talk about returns, it is very difficult to give a generic metric. There are umpteen ways to calculate returns as one can imagine. For example,

  • One could take daily returns and multiply by 252, daily standard deviation and multiply by sqrt(252) to get a risk return profile
  • One could take weekly returns and multiply by 52, daily standard deviation and multiply by sqrt(52) to get a risk return profile
  • One could take monthly returns and multiply by 12, daily standard deviation and multiply by sqrt(12) to get a risk return profile
  • One could just take a mean of calendar year returns and sd of calendar year returns.

In Indian markets, there is no doubt that NIFTY, NIFTY Jnr index assets figure amongst the sought after assets. Also with Gold witnessing a dramatic rise year after year , it is attracting hordes of investors too. Lets look at these assets from a risk return perspective and understand the importance of the scale for returns calculation

Let’s look at these assets over the last 5 years

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Takeaways

  1. Weekly annualized scale for Gold gives a completely different picture as compared to Daily annualized and Monthly annualized. The gold returns are about 5%. These numbers are important as one sees different numbers quoted in the media under different circumstances.
  2. NIFTY Jnr is more risky than NIFTY. It is pretty obvious point as the mid cap is going to be more volatile than large cap.
  3. NIFTY and NIFTY Jnr daily returns annualized have almost the same risk return whereas monthly annualization shows that NIFTY has a better sharpe ratio than Jnr.
  4. Weekly scale - It is important to realize that distributions under weekly scale look so so different. Aggregation at this scale and metrics resulting from it paint a different picture

Let’s look at the same graph after removal of 10% of outliers

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Takeaways

  1. Daily Scale return profile changes completely for Nifty and Nifty Jnr.
  2. Weekly returns annualized for Nifty and Nifty Jnr starts making sense as the numbers are somewhat comparable to daily annualized and monthly annualized
  3. One thing that stands out is that Gold gives about 15-20% returns whichever way you slice and dice daily and monthly data.

However this is just the beginning of looking at scales. For a realtime investors who want to stay put for an year, these metrics do not make sense as they would be interested in looking at returns between t1 and t2 where t1 could be any day of the year and t2 is accordingly 252 trading days away from t1. These are not rolled returns as rolled annualized returns have a different calculation. For lack of better terminology , I will use rolled returns to mean that returns between sets of ordered pairs (t1,t2) in the sample where t2-t1 is 252 days. Now amongst such ordered pairs, there are again three ways to calculate returns.

  • One can take daily returns between t1 and t2 , add up , call it annualized returns , roll it on each day, , form a sample and compute stats
  • One can take weekly returns between t1 and t2, add up , call it annualized returns, roll it for each week , form a sample and compute stats
  • One can take monthly returns between t1 and t2, add up , call it annualized returns, roll it each month , form a sample and compute stats
  • One can take point in time value returns between t1 and t2, call it annualized returns, roll it on each day, form a sample and compute stats

If one computes metrics as described above for the period 2005 to 2009 , here is how returns look

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Takeaways

  1. Weekly scale still paints a different picture
  2. Daily returns and weekly returns look similar though the returns for each of the asset is shifted downwards by a specific amount
  3. The last graph in the above illustration is probably useful as it uses point returns between ordered pairs(t1,t2) for every data point . If one thinks about it, this is what an investor with an expected holding period of 1 year would get .

There are umpteen other scales at which the data can be aggregated.

So, sharpe ratio of the assets reported in the media with out mentioning the proper definition of the scale used , is very dicey to interpret. Depending on what one wants to say, one can combine risk return metric at the appropriate scale and can use to further an opinion about the asset.