In this course, we will discuss fundamental principles of trading off risk and return, portfolio optimization, and security pricing. We will study and use risk-return models such as the Capital Asset Pricing Model (CAPM) and multi-factor models to evaluate the performance of various securities and portfolios. Specifically, we will learn how to interpret and estimate regressions that provide us with both a benchmark to use for a security given its risk (determined by its beta), as well as a risk-adjusted measure of the security’s performance (measured by its alpha). Building upon this framework, market efficiency and its implications for patterns in stock returns and the asset-management industry will be discussed. Finally, the course will conclude by connecting investment finance with corporate finance by examining firm valuation techniques such as the use of market multiples and discounted cash flow analysis. The course emphasizes real-world examples and applications in Excel throughout. This course is the first of two on Investments that I am offering online (“Investments II: Lessons and Applications for Investors” is the second course). The over-arching goals of this course are to build an understanding of the fundamentals of investment finance and provide an ability to implement key asset-pricing models and firm-valuation techniques in real-world situations. Specifically, upon successful completion of this course, you will be able to: • Explain the tradeoffs between risk and return • Form a portfolio of securities and calculate the expected return and standard deviation of that portfolio • Understand the real-world implications of the Separation Theorem of investments • Use the Capital Asset Pricing Model (CAPM) and 3-Factor Model to evaluate the performance of an asset (like stocks) through regression analysis • Estimate and interpret the ALPHA (α) and BETA (β) of a security, two statistics commonly reported on financial websites • Describe what is meant by market efficiency and what it implies for patterns in stock returns and for the asset-management industry • Understand market multiples and income approaches to valuing a firm and its stock, as well as the sensitivity of each approach to assumptions made • Conduct specific examples of a market multiples valuation and a discounted cash flow valuation This course was previously entitled “Financial Evaluation and Strategy: Investments” and was part of a previous specialization entitled "Improving Business and Finances Operations", which is now closed to new learner enrollment. “Financial Evaluation and Strategy: Investments” received an average rating of 4.8 out of 5 based on 199 reviews over the period August 2015 through August 2016. You can view a detailed summary of the ratings and reviews for this course in the Course Overview section. This course is part of the iMBA offered by the University of Illinois, a flexible, fully-accredited online MBA at an incredibly competitive price. For more information, please see the Resource page in this course and onlinemba.illinois.edu.
ASSIGNMENT 2 (Lesson 1-8): Calculating More Efficient Portfolios
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From the course by University of Illinois at Urbana-Champaign
Investments I: Fundamentals of Performance Evaluation
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University of Illinois at Urbana-Champaign
257 оценки
Course 3 of 7 in the Specialization Financial Management
From the lesson
Module 1: Investments Toolkit and Portfolio Formation
In Module 1, we will build the fundamentals of portfolio formation. After providing a brief refresher of basic investment concepts (our toolkit), a summary of historical patterns of stock returns and government securities in the U.S. is provided. We then consider general examples of portfolio choice to highlight the tradeoffs between “risk” and return. We end the module with a discussion of dominated assets and efficient portfolio formation, emphasizing real-world examples and practice in Excel solving for the optimal portfolio given certain constraints (such as the amount of volatility we will accept in our portfolio).
Meet the Instructors
Scott WeisbennerWilliam G. Karnes Professor of Finance
Department of Finance, College of Business
[ Music ]
>> All right.
Lesson 1.8, AKA assignment 2.
Okay? So remember I said module 1 is building
up the fundamentals.
So this will be the only module
where we have two assignments involved.
So in this lesson two parts.
And, as we talked about with assignment one,
the first part is just actually giving you the questions
for assignment two which you're going
to give the old college try to first.
Then after giving it your best attempt, see my discussion,
see the answer key for assignment two.
What's the key point of this assignment?
Getting a measure of how important is it
to add other assets to your portfolio,
and in particular looking at it from, you know,
kind of a U.S. perspective, a U.S. investor perspective.
Is there much benefit to adding gold
if you're already holding U.S. large cap stocks,
if you're invested in the U.S. stock market,
is there much benefit to international diversification,
are the two key points to this assignment
and I think give some valuable lessons
for real world investment practices.
We talked about this before.
I think it's worth highlighting again for this assumption.
Bill Sharpe here designed the capital asset --
One of the people who wrote
about the capital asset pricing model in the sixties.
It provides a nice, you know,
kind of reality check before we get in to doing this work
and coming up with these portfolios.
It's always perilous, you know, paraphrasing him, to you know,
assume the future will be like the past,
but it's at least instructive to find out what the past is like.
Okay? So that's kind of the purpose
of us doing these analyzes.
We're taking assumptions or basing our assumptions
on return distributions that we've measured in the past,
and seeing what that predicts for our portfolio,
assuming these return distributions will continue
in to the future.
If you don't like the assumptions
for the return distribution, the great thing
about the spreadsheet is you can go in and make these
and make different changes and see how the portfolio
or optimal portfolios change.
And then talking further about these assumptions
that when we're -- Historical data are pretty useful
or quite useful when we're looking at standard deviations,
reasonably useful for looking at correlations,
and virtually useless for expected returns.
Now one thing just to, you know, maybe a little caveat to that.
If you're looking at average returns
over a very small time period where there's a big bowl market
or a big bear market, of course the average return there is
going to be far different
from what we've observed historically.
I'm going to be looking at, you know, kind of averages
on return -- in return distributions obtained
over wide samples of data.
So it still might be the case
that the past doesn't really predict what these average
returns are like in the future, but at least it's not going
to be based on like one or two years.
It's going to be based on, you know, kind of, you know, 20,
40 years worth of data.
So this assignment is going to have two parts.
Two portfolio allocations, six questions total.
So when we're looking at asset allocation we first start
out with small and large, small, large value,
and growth was another example we considered.
Now let's expand it up to five assets.
So we're maximizing the optimization routine
or spreadsheet that I put in.
Remember I created rows and columns
for five different assets.
So we're using all of them
and now we're adding gold to the mix here.
So it doesn't make sense to add gold to the portfolio.
So we're going back 40 years.
Okay? 40 years' worth of monthly data.
And this data to use for your assignment is contained
in the spreadsheet.
You know, the name says what it is.
Efficient frontier, large, small, value of growth, gold.
So use this spreadsheet
to do the first part of assignment two.
We get our data on stock returns.
Large stocks, small stocks, value stocks, growth stocks,
again from the Ken French Data Library
which he generously posted online.
Large, small are looking at the top 10% and bottom 10%
of firms raised on the size
of the market value of their equity.
Value and growth are looking at the top 10% and bottom 10%
of firms ranked by their book to market ratio.
So the top 10%, think of the cement company,
a high book to market value where there's a lot
of tangible assets in place.
For the growth stocks, bottom 10% of book to market.
Think of the internet startup with a great idea
that investors are excited about,
but there aren't actually any tangible assets in place except
for maybe a computer server or just a, you know --
kind of an intangible little property or like that.
But most of the assets are intangible in nature
for the growth stocks.
And we add to this now gold price data
from which we can calculate the return on gold
from the Deutsche Bundesbank bank data repository.
So we have monthly data over 40 years.
So I guess that's 480 monthly observations of returns
from these 5 asset classes.
We can calculate average returns, standard deviations,
correlations across these assets.
Okay. So let's look at the questions that I'd like you
to tackle given the data assumptions
that I give you in the spreadsheet.
Okay? And remember those assumptions are derived
from the historical distributions
over the 40 year period, 1975 to 2014, for these asset classes.
So question one.
Suppose that you're currently 100% invested in large stocks
and you cannot short --
So portfolio wage cannot be negative.
So your current situation, 100% in large stocks.
You like the risk of large stocks.
So you may change your portfolio,
but you don't change a standard deviation of the portfolio.
What portfolio maximizes expected return subject
to having the same risk level of large stocks?
What's the expected return in this case?
And what are the portfolio [inaudible]?
What is a new portfolio?
And then how much are returns expected to increase
if you switch from large stocks to this new portfolio?
Another way of saying this is, "How dominated is large stocks
in this efficient frontier?"
Okay? Question two.
Suppose you can short assets now.
Okay? So it's just like question one,
only question two, one difference.
Let's highlight that here.
Now you can short assets.
So the exact same question we had before,
but now you can short assets.
You like the risk of large stocks.
Okay? So what is the optimal portfolio, given you can short,
where you maintain the same risk as large stocks?
Okay? What's that portfolio allocation?
Okay? When you put this portfolio together,
which asset do you short?
Okay? When you're allowed to short and come
up with a portfolio that gives the highest return subject
to having the same risk as the large cap fund,
what asset do you short in this portfolio?
What asset has the biggest increase in portfolio weight
when you go from the scenario of you cannot short,
when you go to the scenario you can short?
That's the second part of the question here.
Which asset has the biggest increase in portfolio weight
when you go from cannot short to can short examples?
Okay? So what's the benefit at the end of the day when you go
from question one to question two, what's the benefit
in terms of, you know, higher expected returns?
Okay? By being allowed to short.
And then, given this benefit and higher expected returns,
is it worth allowing the investor to short?
So, you know, do you have a big increase in expected return
of the portfolio by being allowed to short
or is there a small increase?
When you're allowed to short, what asset do you short?
What asset increases a lot positively
in terms of portfolio weight?
Why is that the case?
Question three.
Let's go back to suppose you cannot short.
What's the expected return, portfolio standard deviation
and portfolio composition of the portfolio
that maximizes a Sharpe ratio?
Excess return of the portfolio divided
by the portfolio's standard deviation.
Does gold have any part in this portfolio?
If it does, why is gold a part
of the maximum Sharpe ratio portfolio?
If gold is nowhere to be seen, its portfolio weight is 0,
given you can't short.
Why is gold not a part of it?
So that's the first half of the assignment.
The first three of the six questions.
The second part is the great thing about this course is,
you know, students from around the world.
So let's consider is there a benefit
to international diversification.
When it comes to traveling and meeting folks,
the answer's definitely yes.
But how about in terms of financial investments here?
So asset allocation with international stocks.
Here we're going to refer to this spreadsheet,
efficient frontier U.S. international.
That spreadsheet you're going to use
for the second part of assignment two.
That has the average return, standard deviations,
correlations between U.S. index [inaudible] Japan [inaudible]
stock market, Asia Pacific excluding Japan, and Europe.
And this data's available
on the Ken French Data Library starting July 1990.
So the weird starting date is just
because that's the first month we had the data.
Through 2014.
So, you know, what is this?
Almost 24-25 years' worth of data that we have here,
monthly data, to do the correlations and stock returns,
calculate standard deviations,
averages across these three regions of the world.
All right.
So question four on the assignment,
this is the first question regarding international
exposure, but question four on assignment two.
So it's well known that there's a home bias in investing.
People tend to invest in stocks and assets
in the country where they're from.
So let's say, you know, we're from the U.S. and we have 100%
in the U.S. stock market.
And we like -- Kind of we're comfortable with the risk
of investing in U.S. stocks, but we're open
to an alternative portfolio as long
as the portfolio standard deviation is the same
as U.S. stocks.
So this is, you know, kind of asking,
"Given a portfolio's standard deviation, it's the same
as U.S. stocks, what portfolio can we put together
with international exposure
that gives us the highest possible return?"
Okay? So maximize the return given the risk
of the U.S. stock portfolio.
What is -- What are the components of that portfolio?
What is the return?
What's -- We know the standard deviation is the same
as the U.S. stocks.
And then kind of the key question is,
"Does this portfolio offer us much higher return
than the scenario where we're 100% in U.S. stocks?"
Question five.
Again suppose you cannot short.
Okay? What's the expected return and standard deviation
of the portfolio that maximizes the Sharpe ratio?
What are the portfolio weights?
Okay? Does Japan have any part in this portfolio
that maximizes a Sharpe ratio?
Okay? If yes, why is Japan part of the portfolio?
If no, why is Japan not?
So what's a portfolio that gives us the biggest bang
for the buck, the biggest Sharpe ratio?
Does Japan have any part in it?
Question six.
Again suppose you cannot short.
Japan has, you know, not performed well
over the last 25 years.
So when you look at their assumptions
for returns, they're very low.
What if we change that assumption
so Japan has the same projected expected returns
as Asia Pacific?
So we bump that monthly return for Japan up to 0.96% per month,
the same as Asia Pacific.
What's the maximum Sharpe ratio now with this change assumption?
What is a portfolio that gives us this maximum Sharpe ratio,
expected return and the standard deviation?
So as we talked about with assignment one, it's, you know,
kind of always good to be curious,
but not so much in this case.
You know, what's our rule?
Do the assignment first.
Give it the college try.
After you do the assignment you're free to, you know,
kind of go in, look at my discussion of the assignment.
If you want to change your answers
after seeing my discussion, that's fine,
but try it on your own first.
Right? It's in your own interest to see --
to get your knowledge of the material.
Then reviewing the answers is fine.
Before you grade or review other people's work,
please look at my discussion so you get a better sense
of what answers to look for and what the correct responses are.
Hopefully your first attempt
and my answers are perfectly correlated with each other.
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