Concentration and Diversification of Portfolio

Let`s End the constant fight between emotion and logic

Many times we try to get a comfort from downside risk of market by diversifying a portfolio, as our general belief is that, if the portfolio is diversified, than one stock may manage to cope up the loss/ gain of another stock. So, the first thing we all know is that the diversification is important to mitigate extraordinary sector specific or stock specific risk from portfolio, apart from market specific risk. But, the question that we forgot to ask ourselves is that, How much diversification should be there, or logically how much diversification is optimum for mitigating all the risks apart from market specific risk from the portfolio.Someone suggested this stock is good or may be you researched any company and found its story convincing and then bought the stock in your portfolio without assessing the weightage and the number of script you already hold in the portfolio. Thus you ended up with either very high or very low impact on returns of the portfolio.

So, today statistically, I will try to answer the former query regarding how much script one should hold optimally in the portfolio to control risks except market risk. (We will talk about weightage/allocation of script in next blog)

Lets understand and try to solve this question by one simple example. Lets say, You have a portfolio having ‘n’ number of scripts in equal weightage. Now, if any script goes down by 20%, what should be the impact on your portfolio? (Read this twice, as your understanding of the article is dependent on understanding of this question.)

The impact on the portfolio value(%) = Allocation of script(%) * % down/up of that script

That means, if any script goes down by 20% and if you are having only “1” script in the portfolio, then the impact on your portfolio would be 20%. Now, if you are holding “5” scripts having equal allocation, then the impact of 20% down in one script would bring down portfolio by only 4% and so forth. See the below table for better understanding.

Table :

Assumption :

1. 1. Equal weightage in all scripts.
2. Today, one script of the portfolio goes down by 20%.

So, what would be the impact on the portfolio:

Lets see this story in the chart :

What do you infer from the above data?

I think,the above chart is self explanatory. But, for non-financial people , let me explain what this data depicts.

Primary finding :

Whenever, we increase the number of scripts, it reduces the impact on the portfolio of any fluctuation in the individual script .

Now, New question arises,

It is well understood that, for every addition of new script, the impact on portfolio reduces, but the question that is now  still left unanswered is How much ?

For this purpose also, I have one another table.:)

And the story in the chart looks like this :

Secondary Finding from the chart is :

For every same no. of increment in the script the impact of fluctuation reduces in the portfolio but at a diminishing rate.

 

That means, you can not reduce the impact on the portfolio by every “one” script increase in portfolio as diversification will not work in your favor after certain point.

For example,

Reduction of impact in portfolio due to increase of script from 5 to 10 (change in incremental impact=16%) is not same as reduction of impact in portfolio due to increase of script from 20 to 25 (change in incremental impact=0.20%). That means if you diversify the portfolio from 10 script to 25 script, then you can reduce the impact of individual script on your portfolio by 80 times (16%/0.20%).

Now let’s take another example,

Reduction of impact in portfolio due to increase of script from 15 to 20 (change in incremental impact=0.33%) is not same as reduction of impact in portfolio due to increase of script from 35 to 40 (change in incremental impact=0.07%). That means if you diversify the portfolio from 20 script to 35 script, then you can reduce the impact of individual script on your portfolio by only 4.7 times (0.33%/0.07%).

So, in above two example, even though the increase in number of script is same but the impact is drastically different. That`s why this question needs to be answered.

Now Lets move forward to third and the final question, that is , What should be the optimal allocation of the portfolio ?

From the tables and statistical calculations as presented above, I would like to conclude that optimal portfolio allocation should be somewhere around 20 stocks for the diversification to work in your favor. Both, very less and very high diversification can harm/reward you in any direction.

Premise of the above statement:

1. Here, I assumed that the all the scripts are in same proportion.
2. How much to concentrate and diversify is a personal choice of the investor. Here I just wanted to show, what statistics/logic says. Nevertheless high Concentration/Diversification can also work in your favor.

So, next time, whenever, you buy any stock, or anyone suggests you to buy a stock, first stop ,think and then act ,keeping in your mind the science of diversification and reap the optimal returns from your portfolio.