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

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来自 Rice University 的课程

Portfolio Selection and Risk Management

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Rice University

Portfolio Selection and Risk Management

238 个评分

课程 2（共 5 门，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.

从本节课中

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

与讲师见面

Arzu Ozoguz
Finance Faculty
Jones Graduate School of Business

Okay, so what have you learned so far from this discussion?

Well, if you thought that these are the expected return on volatilities for

the US and Japanese equity markets and

you could form these portfolios by mixing them together.

What's the main insight?

If this is the data that's given to you and you can combine these portfolios.

Well, clearly you should never hold a 100% US portfolio, right?

As I have illustrated, holding

a mix of the Japanese and US equity market strictly dominates

a 100% invested US portfolio.

So now let's add.

The UK equity market into the mix, okay?

So, we can plot the equity, the UK could have markets average return and

volatility in the same graph, all right?

And in this graph it's represented by the star, so as this is from the given data.

So now, what happens when we combine all three equity markets into a portfolio?

Okay?

So the lighter line shows you the possible combinations that we can

create by holding a mix of the US and the Japanese equity markets.

The blue line now shows you the minimum variance frontier,

the local support folios that deliver the minimum variance, right?

From holding the three markets, the US, the Japanese, and the UK market.

Now you see that the minimum variance frontier expends in two ways, right?

The wings expand outward, right?

And the minimum variance portfolio,

sort of the left most point, shifts a little bit towards the left.

You can barely see it on this graph, why?

Well, remember,

adding another security into the mix that is less than perfectly correlated.

Increases the amount of risk you can diversify away and

reduces the portfolio risk, right?

So for example, when you could achieve this expected return

by the holding a mix of the US and the Japanese market for

this given little of risk by combining the three equity markets together.

Now you can actually achieve a higher reward,

a higher expected return for the same level of risk.

Now what if we add the rest of the G5 countries into the mix?

Let's now add also Germany and

France into the picture, okay?

So now, what do you see, well, what you see is the minimum

varies frontier expands even further, right?

There is a considerable leftward shift in the front here,

the minimum variance portfolio has shifted leftward.

And the wings have become even wider, providing a greater reward,

greater expected return, for the same amount of risk.

You also see something interesting, something really interesting, right?

Notice that all individual equity markets, they are inside the frontier.

They lie inside the frontier, not on the frontier,

they are inside the frontier, what does that mean?

Well, that means all individual assets are dominated all

individual equity markets, in this sense, are dominated by

the diversified portfolio combinations that lie on the frontier.

In other words, no individual market should be held by itself, right?

Diversification helps remove the specific risk,

the equity market specific risk and reduces the all risk of the portfolio.

All right, so in this lecture,

we look at how diversification works using equity market data from G5 countries.

Your take away should be that there are large diversification

benefits when there are low correlations in markets.

You also learn the definitions of minimum variance frontier and

what an efficient portfolio is.

The key insight here is that individual assets lie inside the frontier or

another words diversified portfolios always do better than individual assets.

Because diversification removes or eliminates the idiosyncratic risk and

reduces the overall risk of the portfolio.

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