Historic Volatility Calculation

Dynamic replication of option price requires a key ingredient, volatility. Often we get into arguments about using Implied market volatility, Expected volatility (could be forecast/ prediction) or just historic volatility.

I was just trying to calculate historic volatility of major currency pairs and the Indian and World indexes. At first I thought using daily closing prices would be the most logical method. But later wanted to see if there is significant difference between calculations done on closing prices vs. opening and day high and day close.



I was expecting more or less same volatility figures for different data. But to my surprise the volatility figures based on Day high were significantly less volatile across markets and benchmarks.



The effect is more pronounced in stock Indexes like NSE Nifty, BSE Sensex and foreign indexes like Nikkei 225 and the Dow Jones. This is something very counter intuitive because in the last year all indexes have gone down but still the market highs from one day to other are less volatile compared to Open and High data.

The volatility was calculated by using daily log returns for past 256 data points (roughly 1 yr with 5 market days and 5 holidays)

The Currrencies are Pound, Euro, Yen and Swedis Krona all against USD.

Rupee Depreciating!

In the latter half of the year Rupee has weakened against the Dollar significantly. Black line in the graph is USD/INR which has appreciated from close to 40 Rs for a Dollar in April to about 50 Rs.

At the same time it is argued by some that USD has strengthened across all currencies. Implying that INR has not weakened much its just USD showing lot of strengthening. The red like shows USD index which is trade weighted index of USD against major currency pairs. This like shows performance of USD against other major currencies like Euro, Pound and Yen etc.

There is a close association in the upward movement of Dollar against Rupee and against all other major currencies (in other words the black and red lines)

Fortune 2007 Index : Analysis

Two Fortune India Index was created by using two different methods. One was by using equal weights for all the 39 companies that were selected. Click here to read more about the original Index. The second method gave weights equal to the market cap of each individual share on the particular day. In other words the second portfolio was assumed to be dynamically adjusted to have weights depending upon the market cap of the shares.




The returns calculated was the log return for the entire period starting from beginning of year to end of October. Similarly Beta was calculated by using the daily log returns.

It was found that the returns were as high as 80% in case of equal weights compared to only 23% and 26% for Sensex and Nifty. At the same time what was more interesting was that the Beta of the Index was very low around 0.82. If Beta is taken as the measure of risk (CAPM) then the alpha, or the excess return created for the level of risk taken (beta) would be very high.

Fortune India 2007: Index

Fortune India 2007

Indian stock market has gone up by close to 30% from the beginning of the year. This upswing in the market has resulted in almost all sectors doing phenomenally well. The growth story is not just applicable to the Large caps but also to the mid caps and the small caps. In this kind of a market picking a portfolio that makes more money than the Fixed deposit rates (close to 10% per an) is not at all difficult, but beating the indexes like Nifty and Sensex would be the thing that fund managers look forward to.

Picking a basket of shares like the Sensex (top 30 shares by market cap) or Nifty (top 50 by market cap) would be the ideal thing to do. But recently I found that that in Prowess database there is a group of companies called to Fortune India list. This list has selected companies as per the fortune rankings. I thought this would be a very good method to pick the top companies in the country and as long as the stock market is doing well this index must also perform better. The companies in the list are as following:



Watchout this space for more analysis to see how sucessful is it to invest in such index.