It’s definitely diversity but not a hodgepodge that helps you sail through all the unforeseen tempests.
Diversification across various classes of stocks based on industries, size, value vs. growth etc. within a portfolio helps an investor to minimize risks through summing up different risk behaviours of different stocks while keeping contribution of their respective return unaffected. So an investor has a freedom to construct his portfolio in a manner that risk is minimized and return is maximized.
So early as in 1952 Harry Markowitz changed the whole mindset of all investors who used to measure their success by the performance of each of their stocks separately. He made it clear that one should not concern if some of the stocks did not show up well over a period of time subject to that it is compensated by the rewards of others. In brief, it is not the individual stock but the whole bunch of different stocks called portfolio that should be under purview.
Markowitz showed how an investor can reduce the standard deviation of portfolio return by choosing stocks that do not move exactly together.
Now, if we draw a graph with Risk (standard deviation of security/portfolio) on X-axis and Return on Y-axis the efficient portfolio of given stocks would be that which lies upper and left as much as possible.
See the graph.
It is really a matter of choice which one of the efficient portfolios is best suited to you depending upon the level of your desire of return and aversion to risk. If you love to play with security market ups and down you are most likely to pick up the portfolio which is expected to go uppermost point with least regard to its dangerous shift towards right direction. Though most of the people like you and me are very conscious about uncertainties in the market and try to minimize risk and stay left considerably. In any case, there is perfectly no point choosing a portfolio given on the graph which lies lower than O as there is always a better return available on the given risk level as the graph shows.
Expected Portfolio Return is just the weighted average of the Expected Returns of the stocks present in it but Risk (Standard Deviation) has to be calculated by a formula given below.
First we will see how variance is calculated in respect of a portfolio consisting of only two stocks (for the sake of simplicity) and then as we all know that the square root of that will be the standard deviation.
Portfolio Variance = X12σ12 + X22σ22 + 2 X1X2 ρ12σ1σ2
where x1 and, x2 are proportions of stock no.1 and 2, σ1, σ2 are their standard deviations and ρ12 is the co-variance between them.
The another important point is that we can achieve any level of return represented by any point on the curve and even more than that by adding lending and borrowing at government treasury bill rates that is termed as risk-free investment. And so our investment in part can both be positive or negative depending upon whether we choose to buy a quantity of treasury bill, lend money at treasury bill rate or borrow at the same rate. If we lend money or buy treasury bills then our investment in that part is positive and if we borrow money at treasury bill rate then our investment in that part is negative and the risk is zero in both of such cases.
The government treasury bills give less interest than the security market but it is totally risk-free and suppose if we expect our present portfolio will give a return of 20% and treasury bills is giving just 10% then some of us may like to take more risk that is associated with security investment. They may think sometimes to sell the treasury bills under their possession for buying more stocks from the market. Though it is always advisable to keep a good mix of treasury bills and stocks all the while.
Suppose portfolio P consisting of a different number of shares of selected stocks is predicted (based on past data) to have an expected return of 20% and a standard deviation of 18%. We have planned to mix some quantity of treasury bills that give an interest of suppose 10% p.a. on zero risk (s.d.).
Now, if we put half of our investment in market securities as in the portfolio mentioned above and half in the treasury bills then
Return (r) = 1/2 x expected return on P + 1/2 x interest rate = 15%
Variance = Standard Deviation2 = (σ2) = X12σ12 + X22σ22 + 2x1x2 ρ12 σ1 σ2
σ = X1σ1 (since σ2 = 0)
= (.5) 18% = 9%
Now, suppose we borrow money equal to our initial investment at the rate of treasury bill and invest that amount in our portfolio. Then,
Expected Return, r = 2 x 20% - 1 x 10% = 30%
And, Standard Deviation, σ = X1σ1 (since σ2 = 0)
= 2 x 18% = 36%
So, if we assume that there is an option for everyone to lend and borrow to any limit on the rate of treasury bills then the range of investment possibilities can be maximised to a further extent.