Diversification: A graphical illustration with two assets

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Portfolio Selection and Risk Management

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Rice University

Portfolio Selection and Risk Management

233 ratings

Course 2 of 5 in the Specialization Investment and Portfolio Management

When an investor is faced with a portfolio choice problem, the number of possible assets and the various combinations and proportions in which each can be held can seem overwhelming. In this course, you’ll learn the basic principles underlying optimal portfolio construction, diversification, and risk management. You’ll start by acquiring the tools to characterize an investor’s risk and return trade-off. You will next analyze how a portfolio choice problem can be structured and learn how to solve for and implement the optimal portfolio solution. Finally, you will learn about the main pricing models for equilibrium asset prices. Learners will: • Develop risk and return measures for portfolio of assets • Understand the main insights from modern portfolio theory based on diversification • Describe and identify efficient portfolios that manage risk effectively • Solve for portfolio with the best risk-return trade-offs • Understand how risk preference drive optimal asset allocation decisions • Describe and use equilibrium asset pricing models.

From the lesson

Module 2: Portfolio construction and diversification

In this module, we build on the tools from the previous module to develop measure of portfolio risk and return. We define and distinguish between the different sources of risk and discuss the concept of diversification: how and why putting risky assets together in a portfolio eliminates risk that yields a portfolio with less risk than its components. Finally, we review the quantitative tools that help us identify the ‘best’ portfolios with the least risk for a given level of expected return by considering a numerical example using international equity data.

Diversification and portfolio risk3:07

Diversification: A graphical illustration with two assets4:30

Diversification: A graphical illustration with three assets3:06

Diversification: Systematic risk and idiosyncratic risk7:47

Diversification: An illustration from international equity markets (US and Japan only)11:12

Mean-variance frontier and efficient portfolios: International equity investment example (G5 countries)5:18

Meet the Instructors

Arzu Ozoguz
Finance Faculty
Jones Graduate School of Business

Suppose we have two stocks, A and B, and let's plot them in

the expected return volatility graph like this where the x-axis, right,

represents the risk, the volatility, right, measured by the standard deviation.

And the y-axis represents the expected return.

Now, point A, right, represents the risk and

return, the volatility and expected return combination that we would get

if we invested 100% of our wealth in A.

Now similarly, point B in this graph, right, represents the expected return and

the volatility combination that we would get if we invested 100%

of our wealth in asset B.

Now what if we combine them into a portfolio?

Right?

Now let's start by assuming that A and B are perfectly correlated, right?

With a correlation coefficient of positive 1.

Right?

Now what are the risk and

return combinations that we can achieve from combining A and B into a portfolio?

How do we obtain that?

Well, we would obtain the possible combinations by varying

the relative weights on A and B and

then plotting the expected return and risk for each combination.

And if we did that it would look something like this.

Right?

Now notice that, all though it might not look like it,

we get a straight line, right?

Why?

Well this is because in this case and only in this case,

there is no diversification benefit, right?

Only in this case where the two assets are perfectly correlated, right?

The expected return on the volatility happen to be the weighted

average of the two individual values on the two assets.

Okay, now what if A and B are less than perfectly correlated?

Right?

What if the correlation coefficient between A and B let's say is 0.2, right?

It's still positive but close to 0, right?

Now since A and B are not moving completely in tandem, right,

combining them into a portfolio will reduce risk by diversification.

Right?

Again if we plot the expected return on this combinations that we would

get from combining by changing the relative weights on A and

B, they would look something like this.

Okay, now notice that an equally weighted

portfolio, suppose it's about here.

Right?

An equally weighted portfolio, an equally weighted in A and

B on the orange line, right?

On the orange combinations, has less risk than a similarly

equally weighted portfolio on the blue line, right?

And that's because, right, the orange line assumes that A and

B are imperfectly correlated, right, and that helps diversify risk.

Now what if A and B are perfectly negatively correlated?

Right?

Let's say that the correlation coefficient is -1, right?

Now if you again, plug the risk and return combinations by varying

the relative weights of A and B, this time you might get something like this.

Right?

In fact, right,

in this case it is possible to find some combination of A and B.

Where risk is, right, completely diversified away.

This portfolio here has 0 risk.

And again, this is because of the unique nature

of the perfect negative correlation that we assume for A and B.

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