For a beginner in Finance, it can be quite intimidating to get a basic understanding of how volatility comes into play. It's something not easy to visualize and hence understand. I'll attempt to simplify the concept.
Normal Distribution
A lot of things which move randomly can be approximated to be exhibiting Normality. By this we mean that it may vary in such a way that if we were to calculate a standard deviation, the values in the distribution would fall within 1 standard deviation on both sides, 68% of the time. It would fall within 2 standard deviations on both sides, 95% of the time.
Let's say we have an entity whose value exhibits normality with mean 100 and standard deviation 20. This means that there is a 68% probability that the value of the entity will fall in the range -80 and 120. Further, there is a 95% probability that the value of the entity will fall in the range -60 and 140.
How does it apply to stock markets?
For stocks, it can become a bit tricky as there is a constraint of 0. Stock prices can't fall below zero. Hence, it would be wrong to assume that stock prices exhibit normality. However, we can go one step further and look at the daily stock returns. It has been observed that this tends to behave normally. As daily returns can be negative or positive. Over a period of time we can work out a mean and a standard deviation and this would behave normally. Because now we are not looking directly at the stock prices but the logarithm of stock prices (returns), hence we say that stock prices exhibit log normality meaning their logs exhibit normality.
It can be a bit tricky to understand. Let's say that the mean of returns come out to be 1%. While the standard deviation comes out to be 1.50%. Then this means that there is a 68% probability that the returns would be anywhere between -0.50% (1-1.5) and +2.00% (1+1.5). Further, there is a 95% probability that the next daily return would be anywhere between -2% and 3.5%.
The volatility that we are talking about now is actually the historical volatility. The options market helps us observe the implied volatility base on the option premiums for Calls and Puts. Check out the
calculator here. This implied volatility can be quite different than the historically observed volatility value as the implied volatility represents what is currently priced in by the market, depending on market expectations and corresponding supply and demand forces in the options market.
Normalized Vol or bpVol vs Log Normal Vol
Stock markets are actually pretty straight forward when we have some trickier things like Interest rate options. Which Vol do we use there? The concept of volatility actually remains the same. However, it's more about convention in terms of how the market looks at it. Because interest rates are themselves quoted in % terms it can become very confusing to use volatility also in % terms. Secondly, it doesn't make sense to calculate how much 1 standard deviation means in terms of interest rate movements. So, instead of quoting the lognormal vol, often vols are quoted as normalized vols. They are 'normalized' by using the forward rate. Say the 3m USD Libor has a forward rate of 3% and lognormal volatility is 20%. Then,
normalized vol or bpVol = lognormal vol * forward rate
So, normalized vol = 60bps
Because this is often the volatility expressed in terms of basis point movements, it is well known in the market as bpVol. Later when we discuss deeper concepts of Structuring and Trading we'll see how understanding bpVol is very important.
If one thinks logically, of all the people who became known and famous and of all those who lived in oblivion, it would be tough to pick which is the right way to live. After all, life is only a series of experiences. In the bigger scheme of things, we are as big as we choose for ourselves to be. If that one year I spent somewhere was the best year of my life, there are two fighting forces within me. One is telling me to go back and live some more of that comfort that was. The other and the logical one knows that it's not a wise thing to do. For the latter knows that the experiences that I'm creating now are important to give variety to my fabric and give it some color. Think about any particular year in your life and think about the memories you have from that year. Is it that you woke up at 8 o' clock, got ready, went to work? Or do you remember how on that one day, when it rained so heavy that you were all wet only to be told on reaching that school that it's been declared a holiday? I think memories are created by the little differentials that we build in from one day to the other. Some are external of course, but most of them not. And we have to give our life a chance to create more and more of them by trying to vary our experiences.
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The more one reads, the more knowledgeable he becomes. We need to read all this to know the possibilities around us and that awareness gives us a chance to get inspired and create something of value or just something fun. I, myself, have been so busy lately, working 8-10 everyday and then working on this website that it was very tough to manage reading any book for a long while. However, it's only me to blame as one does what one desires to do. An event happened that put me back to reading. Our internet stopped working! I ended up spending the whole day reading a great book. And now I'm left looking for more good stuff to read.
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