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 in MPT (Modern Portfolio Theory) 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** =* X_{1}^{2}σ_{1}^{2} + X_{2}^{2}σ_{2}^{2} + 2 X_{1}X_{2} ρ_{12}σ_{1}σ_{2} ** **

where x1 and, x2 * _{ }*are

*proportions of stock no.1 and 2, σ*

_{ }_{1, }σ

_{2 }are

*their standard deviations and*

_{ }*ρ*

_{ }_{12 }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 the acts of lending or borrowing money 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 sell t-bills / borrow money at the same rate. If we lend money or buy treasury bills then our investment in that part is positive and if we sell treasury bills or 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 almost 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 Deviation* ^{2}* = (

*σ*

^{2}*) =*

*X*

_{1}

^{2}*σ*

_{1}

^{2}*+ X*

_{2}

^{2}*σ*

_{2}

^{2}*+ 2x*

_{1}x_{2 }*ρ*

_{12 }σ_{1 }σ_{2}

** **σ = *X _{1}*

*σ*

_{1 }*(since*

*σ*

_{2 = 0)}* = (.5) 18% = 9% *

Now, suppose we borrow money equal to our initial investment at the rate of treasury bill (or sell tresury bills in our possession to such an extent) and invest that amount in our portfolio. Then,

Expected Return, r = 2 x 20% - 1 x 10% = 30%

And, Standard Deviation, *σ = **X _{1}*

*σ*

_{1 }*(since*

*σ*

_{2 = 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.

**Sharpe Ratio**= Risk Premium / Standard Deviation = r - rf /

*σ*

**CAPM**) they said that

**"Expected Risk Premium varies in direct proportion to beta"**

**APT**) is altogether on a different footing. It says that each stock's return depends partly on pervasive macroeconomic influences or 'factors' and partly on 'noise' events that are unique to that company. And so,

**Three-Factor Model.**

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