Diversification and efficient frontier

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From the course by Indian School of Business

Portfolio and Risk Management

134 ratings

Indian School of Business

Portfolio and Risk Management

134 ratings

Course 2 of 5 in the Specialization Financial Markets and Investment Strategy

This course teaches you the concepts of risk and expected return. This course presents an overview of the basic concepts and techniques used to construct financial portfolios. You will learn about the investment process and get a very good understanding of economic, industry, and company analyses. We will also look at understanding and interpreting major portfolio management and risk concepts. Through this course, you will discover the basic concepts of Modern Portfolio Theory. In the second half of the course we explore the frameworks to measure investment performance, as well as the various measures of investment performance. Finally, you will learn how to measure performance of equity, bonds and hedge funds. After completing this course, you will be able to appreciate the details that go into the creation of investment portfolios.

From the lesson

Concept of risk and return

The second module introduces the student to the concept of portfolio math and the concept of diversification. The student is taught how to construct the investment opportunity set with risky assets and risk-free asset.The student is then introduced to the concept of Market portfolio and the Capital market line.

Diversification and efficient frontier5:23

Two fund separation6:39

Diversification revisited4:57

Meet the Instructors

Ramabhadran Thirumalai
Assistant Professor
Indian School of Business

Learning outcomes.

After watching this video you will be able to, understand the difference

between the mean variance frontier and the efficient frontier.

Define the minimum variance portfolio, that is MVP.

Diversification and efficient frontier.

In the last video,

we saw what happens when we combine two risky assets into a portfolio.

We saw specifically, that for some combinations of x and

y the standard deviation of the portfolio

is lower than the individual standard deviations of x and y.

This is the idea of diversification.

In this video, we will discuss the idea of diversification in a little more detail,

and introduce the concept of efficient frontier.

Let's revisit the picture from last class.

Look at the black line when the correlation is plus one.

In this case, the standard deviation of all combinations of x and

y are always greater than that of asset x.

This shows that diversification is not possible when

the asset returns are perfectly positively correlated.

Diversification is possible only when asset returns are less than

perfectly positively correlated, that is, row is less than plus one.

Next, look at the pink curve when the correlation between asset returns is

a negative one.

There is one point where the curve touches the vertical axis,

at this point, the risk is zero.

This says that when there is perfect negative correlation between two

assets returns, one particular combination of two risky assets is riskless,

in other words, this combination completely diversifies away all risk.

Let's extend the two risky asset case to three

risky assets by adding another risky asset z.

The expected returns and standard deviation for x are still 10% and

7%, respectively.

The numbers for y are 20% and 10%, respectively, and

those for z are now 15% and 12%, respectively.

We're also given that the correlation between x and y's returns is 0.1.

That between x and z is 0, and that between y and z is 0.9.

First, let's plot the investment opportunity set for

each pair of investments.

The blue curve is for x and y, the green curve is for

y and z, and the pink one is for x and z.

With each pair of risky assets,

the investment opportunity set is just a curve or a line.

What if we look at investing in all three assets at the same time?

Then the investment opportunity set is a whole area.

In the picture, this is the entire area within the black curve.

Each point within this area,

represents a possible combination of x, y, and z.

The black curve is called a mean variance frontier and

plots the optimal combinations of x, y, and z.

What does optimal combination x, y, and z mean?

The mean millions frontier joins portfolios of x,

y, z that yield the least risk at each level of expected return.

Another way of looking at optimal combinations is what is

the maximum expected return at each level of risk.

Looking at the optimal combinations this way, at each level of risk,

the expected return on the top part of the mean variance frontier is always

greater than the expected return on the bottom part of the mean variance frontier.

In other words, the top part always dominates the bottom part.

If we exclude the bottom part of the mean variance frontier

the the top part is called the efficient frontier.

It maximizes the expected return at each level of risk, and

minimizes risk at each level of expected return.

In terms of risk return combinations, no risk return combination

to the left of, or above the efficient frontier, is feasible.

An important point to note is the portfolio called MVP,

it stands for the global minimum-variance portfolio.

Using x, y, and z, this is the one portfolio that has the least variance

of risk across all portfolios in the investment opportunity set.

Given risky assets x, y and z,

no combination of these assets will help us achieve a lower risk.

In our example of three risky assets, how do we determine the efficient frontier?

We will talk about two-fund separation and

how it may be used to draw the efficient frontier next time.

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