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.
DISCUSSION OF ASSIGNMENT 4 (Lesson 3-7): Analysis and Recommendation of 50 Balanced Funds, 1995-2014
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来自 University of Illinois at Urbana-Champaign 的课程
Investments I: Fundamentals of Performance Evaluation
250 个评分
从本节课中
Module 3: Testing the CAPM, Multifactor Models, & Market Efficiency
In Module 3, we will discuss different asset-pricing models, the pros and cons of each, and market efficiency. In particular, we will test the effectiveness of the Capital Asset Pricing Model (CAPM) and examine survey data concerning its use by chief financial officers (CFOs) of firms. Predictable patterns in stock returns, such as the size and value effects, will also be examined and the Fama-French 3-Factor Model will be introduced. Market efficiency will be discussed in this module, as well as its implications for the asset-management industry and observed patterns in stock returns.
与讲师见面
Scott WeisbennerWilliam G. Karnes Professor of Finance
Department of Finance, College of Business
[ Music ]
>> All right, let's discuss assignment 4, this was analysis
of the 50 balanced funds.
The key kind of motivation behind this assignment was
to test your understanding of the capital asset pricing model,
the 3-factor model, differences between the two,
what differences in outflows
between the capital asset pricing mode
and 3-factor model, what they represent.
To do this I gave you return data over the last 20 years
for 50 balanced funds with, you know, varying degrees
of performance, varying degrees of investment styles.
I reported in the Excel spreadsheet excess returns,
returns in excess of the treasury--
one year Treasury bill rate on an annualized basis,
it's useful in this discussion.
Kind of going back if I was creating this spreadsheet now I
probably would've just given you the raw returns.
So for the average 50 balanced funds in the spreadsheet,
the average raw return was 7 1/2 percent per year.
The excess return of 4.8 plus the 2.7 here risk-free return.
So the CAPM beta 0.52 on average and the CAPM alpha
of 0 percent on average.
So the average excess return of the 50 funds was 4.8 percent
to get this to a total raw return, add in the 2.7 percent
of the risk-free rate to give us this average fund raw return
of 7 1/2 percent per year.
Across the funds CAPM beta is about 0.5 0.52 to be precise
and the CAPM alpha the average of that
across the 50 funds literally 0.
Okay comparing this to, you know, kind of the overall,
you know, kind of environment here,
what were other assets yielding, stock market 12 percent
on average over this 20 year period, 1995 to 2014.
Treasury bills 2.7 percent on an annual basis.
Small stocks outperform big stocks over 1995 to 2014,
on the order of about 2 percent per year,
while value beat growth on the order
of about 3 percent per year over this period.
So here again we're looking at the raw returns per year,
so this is basically taking the excess return
from the spreadsheet, adding back in the risk-free rate,
which averaged 2.7 percent over this period.
Now these numbers down here
on the X axis are not fund ID numbers instead this is just
kind of the ranking of the funds.
One is giving you what the lowest return fund,
50 is just giving you the highest return.
So what do we see for these balance funds
that have some combination of US stocks
and Treasury bills as investments?
Remember, the average raw return was 7 1/2 percent that's kind
of roughly what the median return is here.
The high return is just under 10 percent of the funds
and the worst-performing fund yielded a raw return
of 4 percent per year.
Now what if we put these fund over 1995 to 2014,
using the annual data.
What if we put them through a capital asset pricing model
calculated in alpha and beta to benchmark it just because,
you know, different funds have different equity tilts,
maybe investing in different types of equities?
So what if we adjust for the systematic risk
of the different investments across the balance funds.
Then we see remember the average alpha and this is, you know,
alpha from the CAPM in percent per year.
And remember this is the average over a 20 year period right.
These were based on returns over 1995 to 24, so it's not a one
or two year snapshot,
these alphas were estimated using annual data
over a 20 year period.
So the average alpha was 0.
You can see here for, you know, kind of the median fund,
it looks like the alpha is slightly less than 0,
but around the middle
of the distribution here the alphas are pretty close to 0.
The best-performing fund in terms
of this risk-adjusted return is, you know, a little over--
just under 2 1/2percent per year.
The worst-performing fund is underperforming its benchmark
by three percentage points per year on average
over a 20 year period.
So this is historically has really been a dud
of an investment here.
Okay so let's do some analysis of these, you know,
various balance funds and what these various, you know,
kind of parameters from the models represent.
The CAPM beta, this is giving us the average tilt
of the portfolio toward equities.
So for example, a portfolio that's 50 percent US stocks,
50 percent Treasury bills would have a beta of 0.5 okay.
If it was 80 percent stocks, 20 percent Treasury bills
that would have a beta of .8 okay.
Where I'm assuming when I say US stocks invested
in the US stock market index.
Now if we look at the CAPM beta across the 50 balance funds,
it varies from 0.32 to 0.68 okay.
So that means for one fund the systematic risk
of that fund is equivalent to a fund that's 1/3
in the US stock market, 2/3 in he risk-free rate,
where there's another fund that exactly the opposite.
On average it has the same systematic risk
as a fund that's 1/3 in Treasury bills,
2/3 in the US stock market.
Okay the CAPM alpha, so if we look at, you know, let's adjust.
We want to compare fund managers
across the different balance funds, some funds are going
to have high returns because they're taking
on higher risk okay.
They're investing more in Tiffany's, less in McDonald's
or they're investing more in stocks in general less
on T-bills, so on average we'd expect those fund managers
to generate higher returns
as because they're taking on higher risk.
The CAPM alpha is adjusting for that and by risk
in the CAPM model it's just talking about systematic risk,
market risk, sensitivity of the performance of your [inaudible]
or security to the overall market.
Once we, you know, account for the appropriate CAM benchmark,
the systematic risk of investment, the equity tilt
of the fund, we're getting outperformance as high
as 2.3 percent per year again on average
over this 20 year period.
And underperformance is low
as a -3.2 percent underperforming the benchmark
by 3.2 percent per year for one of the funds.
But again, the average
across all the fonts happen to be about 0.
So when we go to the 3-factor model the betas for example
on the small minus big factor, the high minus low
which I would've called value minus growth factor they give us
clues about the underlying investment style
of the portfolio okay.
When we look at the alpha on the 3-factor model that adjusts
to take into account this investment style okay.
So a way to think about when you do the 3-factor model,
fund managers don't get credit for investing
in small value stocks in the 3-factor model that's kind
of taken into account instead of appearing in alpha that appears
in the beta on the size and value factors.
Likewise investment managers are focusing
on large-cap growth stocks don't get penalized for that
in the 3-factor model, we know those are assets or securities
that have underperformed historically, that's taken
into account in the 3-factor model it shows
up in the betas doesn't show up in the alphas.
So, you know, kind of simply investing
in a small value index fund won't yield any alpha
on the 3-factor model, although it has historically
in the capital asset pricing model.
Okay one simple measure that we start off with,
the Sharpe ratio, this is gives us kind
of the simple bang for the buck.
The average excess return of the stock divided
by its standard deviation or, you know,
kind of total volatility on that metric.
Now that isn't differentiating, all risk is kind
of treated the same because the standard deviation
of the returns reflects both kind idiosyncratic risk
and systematic risk.
So the Sharpe ratio, you know, excess return
over the total risk if you will
or the total standard deviation volatility of the investment.
Fund 1, Fund 7, Fund 47 all have particularly high Sharpe ratios
in terms of, you know, bang for the buck,
excess return over the volatility.
How about take into account the market risk of the portfolio,
you know, different portfolios have different, you know,
loadings on equity versus Treasury bills,
some are investing more in stocks, some are investing less.
Those that invest more in stocks given the average stock return
is 12 percent over this 20 year period they're probably going
to do better than funds that invest less in stocks
over this 20 year period.
The capital asset pricing model will take that into account
so we can more fairly compare asset managers of portfolios
that have different investment strategies.
So let's compare for example to illustrate this two funds,
Fund 47, the raw return again,
the excess return plus the average T-bill rate
over the 20 years gives us a raw return
of 9.6 percent for Fund 47.
For Fund 1 the raw return is 8.3 percent,
again it's excess return plus the average annual T-bill rate
gives us this 8.3 percent.
So a difference Fund 47 yielding a higher return than Fund 41,
a difference of 1.3 percentage points per year on average
over the 20 year period,
so a pretty substantial outperformance here.
But what that doesn't take into account,
this 1.3 percent here doesn't take into account is
that Fund 47 is kind of, you know, kind of putting the,
you know, kind of foot on the gas pedal, putting the food
on the accelerator a little more than Fund 1 is.
So for Fund 47 the beta is 0.5, for Fund 1 it's 0.38.
So Fund 47 is generating higher returns, but it is taking
on more risk in that it has a higher tilt toward equities
on average.
So once you take that into account in terms
of the capital asset pricing model in calculating in alpha,
the outperformance relative to the benchmark that takes
into account market risk takes into account the equity tilt.
Both of these historically have done very well.
Both Fund 47 and Fund 41, but now the differences
in their performance risk adjusted is only 0.2 percent
as opposed to this original 1.3 percent.
Fund 47 as an alpha 2.3 percent, Fund 1 has an alpha 2.1 percent.
So another way to think about this, of this difference
in returns of 1.3 percent, 1.1 percent of that, 1.3 minus 0.2,
1.1 percent of that 1.3 is accounted for just differences
in underlying risk of the investment strategies
between the two funds.
So we just talked about two great funds, at least great
in terms of the historical performance.
Fund number 1, Fund number 47.
On the flipside, Fund 23 has performed terribly.
On average it invests 50 percent in the stock market, you know,
reflected by a beta 0.54.
Another way to say this is the risk taken
on by Fund 23 is the same as--
systematic risk take on by Fund 23 is the same
as a fund that's 54 percent invested in the US stock market,
46 percent invested in Treasury bills that's what the beta
0.54 represents.
So the equity tilt for this fund is about average
across the funds in the sample are actually a little higher
than that average beta 0.52.
So a little higher than average equity allocation relative
to the other funds.
Despite that, its performance is the second worst,
its raw return is 4.5 percent per year, the excess return
of 1.8 plus the 2.7, you know risk-free rate,
4.5 percent raw return, second lowest in the group
of 50 even though it has a slightly higher
than average tilt toward equities.
So it's really doing poorly.
The average return across all the funds was 7 1/2 percent.
Once you take into account its tilt toward equities,
it has this benchmark adjusted return of -3.2 percent per year.
In other words, given its tilt toward equities,
on average it should've been yielding 3.2 percent higher
return, 3.2 percentage point higher return
on average per year for 20 years than it actually did.
Instead of generating 4.5 percent given its risk
in investing in equities,
it should have been generating 7.7 percent.
So question one was why are there differences in alphas
across a CAPM model and the 3-factor model
and I identified six funds here with, you know,
kind of dramatic changes here.
Let's kind of go through these funds, you know, one by one.
Fund 7 you see the alpha increases, you know,
by 0.8 percent per year, percentage points per year.
When you go from the CAPM model to the 3-factor model,
what is leading to this increase in the, you know,
kind of outperformance of the benchmark?
Well what the 3-factor model is taking
into account is Fund 7 has a tilt toward growth stocks
indicated by this negative beta on the value minus growth
or high minus low factor.
So this negative coefficient represents
when growth stocks are doing well.
HML is negative, negative times a negative coefficient
is positive.
So in other words, this negative coefficient here means
when growth stocks are doing well that's a period
where this fund is doing well so it has a growth tilt.
Given growth stocks historically have outperformed value stocks,
this 2.1 percent outperformance
in the CAPM is even more impressive,
it's even more impressive
to generate this high return given you're kind
of swimming upstream investing in growth stocks
which have underperformed during this period.
So, therefore, when we go to 3-factor model the alpha goes
up a bit because it's taking into account
that this is a manager who was investing
in growth stocks given this negative coefficient
on the value minus growth factor,
growth stocks have underperformed relative
to value.
So, therefore, we adjust the kind outperformance up
or another way to say it is we lower the benchmark given the
tilt toward growth stocks for Fund 7,
so the 3-factor alpha is greater than the one factor CAPM alpha.
Fund 9 the opposite happens when you go from the CAPM model,
the alpha the outperformance of 1.2 percent per year drops
to 0.7 percent of the 3-factor model.
Well why is this?
Well this is because one of the reasons for the good performance
in the CAPM for Fund 9 was the sensitivity
to small stocks right.
When small stocks are doing well SMB is positive,
positive coefficient on small minus big means this fund is
doing well.
So, you know, one of the reasons
that this fund did well is it invested in this small strategy
which historically has been large-cap stocks,
so we need to make our benchmark a little higher for Fund 9
and the 3-factor model, therefore,
the alpha the alpha falls.
So the performance of the manager
of Fund 9 is less impressive once we take
into account the investment style.
For Fund 26 we have an improvement in performance,
they're negative in both,
but the CAPM alpha minus 1.8 percent, we actually bump
that up to -0.7 percent of 3-factor alpha.
Why, because fund manager 26 was really swimming upstream,
the investment tilt was away
from small stocks toward large stocks given
by this negative coefficient or indicated
by this negative coefficient, also toward growth stocks given
by the negative coefficient here on the HML
or value minus growth factor.
So fund manager 26 seemed to be investing
in both large-cap stocks and growth stocks,
both of them have outperformed so we should lower our benchmark
for this manager when we go to the 3-factor model.
Therefore the, you know, kind alpha is reduced as a result.
So in the case of fund manager 26,
the investment performance is less bad once we adjust
for the investment style that is swimming upstream investing
in both large-cap stocks and growth stocks.
For Fund 27 the, you know,
kind of the investment performance is viewed
as less impressive.
Once we go to the 3-factor model the alpha becomes negative
because this is a manager that was investing in stocks
that historically outperform.
A positive tilt towards small stocks,
a positive tilt towards value stocks.
So, you know, given you were generating an alpha of 0
on the capital asset pricing model that's not very impressive
because you are investing in stocks
that typically have positive CAPM alphas.
The small stocks and the value stocks,
we need to raise your benchmark up when we go
to a 3-factor model, once we do
that your alpha becomes negative here,
performance is less impressive given the investment style.
Fund 31, we can see here by the negative coefficient
and the small minus big factor, the negative coefficient
on the value minus growth factor means Fund 31 is positively
correlated with the performance of large stocks,
as well as growth stocks and we know that both large and growth
over this period underperformed okay.
So this CAPM alpha of 0.1 actually that's not that bad,
so we're going to lower your benchmark given you are
investing in these types of stocks that underperformed.
So the alpha goes from 0.1 to 1, performance is more impressive
when we go to the 3-factor model and we take
into account your investment style.
And then finally, Fund 50 this is, you know,
a fund manager who's doing, you know,
very poorly in the CAPM model in terms of underperformance
by 2 percent per year on average over this 20 year period.
Big tilt towards small stocks and value stocks,
so should be doing pretty well on average in a CAPM,
is generating a negative alpha even though you're kind
of swimming downstream here right.
You're kind of investing in assets
that over this period tended to do well, small stocks
and value stocks, so should be easier going downstream.
But you're underperform-- you're doing poorly in the CAPM World,
which means, you know,
given your investment tilt you're going
to be doing even worse in a 3-factor model
because we're going to raise your benchmark up,
we're going to raise your, you know, kind of hurdle rate up.
Given you're investing in small stocks and value stocks
which historically have done well your kind
of lackluster performance is viewed even worse given your
investment style.
So question two, which of the 50 funds would you most
like to invest in going forward and then three,
which of the funds would you least like to invest
in going forward and why?
Well before I answer this I thought it would be useful just
a few funds that kind of caught my eye, the key thing is based
on past performance some, you know,
kind of notable funds here.
So on the positive side in black,
you know, Funds 1, 7 and 47.
If you look at particularly for Fund 1 it is, you know,
kind has a small allocation to equities, the CAPM beta is less
than 0.5 despite that has a very high Sharpe ratio,
a pretty high raw return at 8 percent per year, CAPM alpha of,
you know, kind of 2 percent beating this benchmark.
So it has kind of low risk, low sensitivity to the market,
but is performing very well so it has this high CAPM alpha.
When you go to the 3-factor model the alpha stays exactly
the same, so that would be consistent with Fund 1 manager
or the manager of Fund 1is a manager that just knows
when to get in and out of the market,
doesn't have a particularly investment tilt in terms
of small big value growth, just is good at market timing.
When to get in the S&P 500, when to get out of it for Fund 1.
For Fund 47 for example, they're taking on more risk
as a result generating a higher return.
This is kind of example we went through earlier
in this lesson comparing 1 versus 47.
If you like kind of investing in large-cap stocks that seems
to be what Fund 47 is given this negative coefficient
on the small minus big beta.
Focusing on some of these, you know, kind of duds based
on the past performance, you know, 23, 42, 50.
You know, Fund 23 we talked about earlier has his
above average tilt toward equities,
but despite that gives this, you know,
kind of second worst raw return leading
to this gigantic negative alpha on the CAPM model.
For Fund 50 it has this big tilt it's investing in small stocks
on average or it's consistent with investing
in small stocks given this positive coefficient
on the small minus big factor.
Positive coefficient on the value minus growth factors,
so consistent investing in small value stocks.
So given investment in small
and value it should be doing pretty well, but it's not,
you know, its CAPM alpha is -2 percent per year on average,
you know, lackluster return.
Once we account for, you know,
kind of swimming downstream investing in assets
over this 20 year period did pretty well,
its 3-factor alpha accounting
for this favorable investment style even worse
down to -3 percent.
But the key issue, how well does the past predict the future,
is past prologue?
That really goes into do you want to simply rely
on your future investment choice being tied to past returns?
So key question, which of these funds would you invest
in going forward, which would you avoid given the
historical data?
The answer, any of them, none of them okay, so say what,
you know, what's going on.
We do all this work and the answer is any of them are fine
to invest going forward or none of them, any of them are fine
to avoid, none of them, you know, what's going on here okay.
Well it turns out each of these funds the pattern
in returns that, you know, was a put into the spreadsheet,
each fund each year I drew a random number between 0 and 1
from a uniform distribution.
So that determined for that fund
for that year what fraction was invested in the US stock market,
what fraction was invested in Treasury bills okay?
So if the number drawn was 0.7 for that fund for that year,
70 percent in the broad US stock market,
30 percent in Treasury bills.
And then another random number drawn for the next year
for that fund, for the next year, for the next year,
for the next year, for all 20 years, then random numbers drawn
for the 20 years for the next fund, so on and so forth.
So I guess 50 funds times 20 years, 1,000 random numbers,
so then with all these allocations between stocks
and the risk-free rate estimate CAPM regression,
estimate 3-factor model, calculate Sharpe ratio just
like you would with any return series okay.
So given these are random numbers uniform distribution
drawn between 0 and 1 the expected value
of that distribution 0.5,
so the expected investment is 50 percent
in Treasury bills, 50 percent in stocks.
Pretty close with this average market data
of 0.52 percent for the sample.
Remember we're drawing from random so it doesn't have,
you know, doesn't have to be exactly 0.5,
but it's pretty close to that.
Now 50/50 US stock market Treasury bill portfolio would
give an average return of 7.3 percent per year
over the period, pretty close to our average of 7.5 percent.
So what's the point, thinking about the analysis
of past fund performance?
All of these numbers were random,
they did not reflect any active decision-making
on market level research or firm level research.
So, you know, I told stories like hey here's a value tilt
for this one, a growth tilt for this one, this one's good
at timing the market, you know, just looking at the past,
interpreting the regression results.
But it turned out the data underlying the regression
results was just driven by a collection
of random numbers okay.
But even though these portfolio allocations were driven
by random numbers the performance
that we observe looks pretty similar to if we look
at the performance of actual mutual fund managers.
So the point is if you're trying
to make investment decisions based on past performance,
particularly you're trying to make investment decisions
for actively managed mutual funds and you're basing
that on past performance, you need to be very careful
because I gave an example here where funds, you know,
some funds have good past performance some have bad,
but it's clearly not predictive of future performance
because it is all driven by a random number generator.
Okay, so the fund that did very well
like Fund 1 could do very poorly in the future
if it just happens to draw bad numbers.
Fund 50 which I believe did very poorly in the past
with the random numbers it happened
to get could do very well in the future.
And in fact, our expectation is all these funds have the same
expected return in the future because we don't know
which random draws they'll get,
whether they get a high equity allocation in the year stocks go
up or whether they get a high equity allocation in a year
like 2008 when stocks fall a lot,
it's just driven by chance okay.
So the ultimate point is it's very hard to differentiate luck
from skill simply looking at past performance okay.
Let me give you another example of luck or skill.
Are there any American, you know, kind of football fans?
Even if you're not you're probably aware of the Super Bowl
which is the championship in which the winner
from the American Football Conference, AFC,
plays the winner from the National Football Conference,
NFC.
They meet up for the ultimate title in the Super Bowl.
So, you know, what are example of some AFC and NFC teams,
2015 super bowl winner, you know,
New England Patriots is an AFC team, Pittsburgh Steelers,
Denver Broncos also AFC teams.
For the NFC I have to go to my home state, you know,
kind of Green Bay Packers here be a famous NFC team, you know,
Dallas Cowboys, Chicago Bears would also be NFC teams okay.
So there's a lot of bets during the Super Bowl on the game,
but there's also crazy bets during the Super Bowl
that have nothing to do with the game.
So people can bet for whether the NFC or the AFC is going
to win the coin toss at the start of the game.
So if the Patriots are playing the Packers, you know,
they did play once in the Super Bowl Packers won the game,
do the Packers win the coin toss,
do the Patriots win the coin toss?
Does the NFC or the AFC team win or you can just bet is it heads
or tails or does the team
that wins the coin toss win the Super Bowl?
All these are bets, so a typical wager would be
like if the gambler is correct they get $100,
if they're wrong they have to pay $105.
So the casino on average is winning $2.50 on this bet here,
the gambler is losing $2.50 on average, but it's maybe just fun
to put this together right, it's just driven by chance.
So the historically profitable strategy that, you know,
has been very lucrative in the past is actually generated
from betting on this coin flip okay.
In particular, the historically profitable strategy is bet the
NFC team in the Super Bowl will win the coin toss.
So if it's the a Green Bay Packers or Dallas Cowboys
or Chicago Bears whoever the NFC team is bet
that they will win the coin toss in the Super Bowl.
Okay the NFC is on a roll,
of the first 48 Super Bowls the NFC has won 32 times or 2/3
of the coin flips, including a streak of 14
in a row, 1998 to 2011.
So for example, the likelihood
of winning the coin toss 14 years in a row like the NFC did
from 98 to 2011, is one in over 16,000 okay.
Another way to think about this
if you placed an original $100 bet in 1998 Super Bowl
that the NFC would win and you kept on doing double or nothing
with that bet, at the end of 2011 that would've gone
to a final balance of $1.6 million.
So this is a pretty lucrative investment strategy.
But other coin flip bets, remember all this is driven
by chance, other coin flip bets aren't as lucrative.
So the first 48 Super Bowls heads 50 percent of the time,
tails 50 percent of time,
literally 24/24 for heads and tails.
Of the first 48 Super Bowls the team
that won the coin flip won the game 50 percent of the time,
the team that won the coin flip lost the game 50 percent
of the time.
So all this is driven by chance it just happens this one bet
based on the NFC has had this nice run,
but obviously that's not driven
by skill it's just driven by luck.
So like if we have, you know, a group of 100 people some
of those will flip a coin and get five heads in a row,
not too many but a few.
Just kind of driven by, you know, kind of the luck
and the randomness of the process here.
So, you know, bottom line luck versus skill pretty hard
to differentiate a lucky money manager
from a skilled money manager.
You know, in particular, you just don't want to look
at past returns and say ah that means, you know,
kinda of good money manager, let me put my money with them okay.
Because we saw that, you know, positive alphas,
very positive alphas on the order of over 2 percent per year
over a 20 year period can just be generated
by random numbers by chance okay.
Assignment 4 shows with these, you know, 50 balance funds
that adopted random investment strategies in terms
of their allocation of equities versus Treasury bills,
some of those fund managers outperform
for a long, long time okay.
So this doesn't mean you shouldn't invest
with active fund strategies, I'm not saying that at all.
What I am saying is if you want to invest with an active fund
and the manager has done well in the past
and you're investing based on that.
Hey good past performance I bet it's going to continue,
do some more research, understand the source
of the mutual fund manager's outperformance,
what's the investment idea, what's being exploited and does
that make sense to you a priori?
Because remember in a fully efficient market some active
fund managers will do well, some will do poorly just
like in the assignment with the 50 balance funds.
If you want to invest in a fund
that will do well going forward you want to, you know,
be sure you understand the investment strategy,
what behavioral bias is it exploiting,
why does it make sense a priori and why did it generate profits
in the past and likely continue
to generate profits in the future.
Okay another factor when we're thinking about active management
and its successes, we remember all the Warren Buffets
of the world, so you think wow investing is
like easy look how well Warren Buffet has done.
We forget all the managers who have done poorly and gone
out of business, it's like a selection bias.
Kind of like value versus growth stocks in terms
of their returns like, you know, at some point Microsoft,
Google when they started out they were, you know kind
of definite growth stocks, Microsoft and Google,
Apple done extraordinarily well.
So it seems like the returns of those companies
on average would be higher
than the cement company, than the value stock.
But while we remember Microsoft, Google and Apple,
we forget the dozens of pets.com of the world that failed,
so kind of a selection bias or a selection bias
in our memory is maybe playing into this as well.
So key lesson is learn from our discussion here
of assignment 4 is you know kind of understanding the differences
between the capital asset pricing model
and the 3-factor model, what the differences in alpha represent,
how the coefficients on the various factors
in the 3-factor model give us clues about at least, you know,
what the potential investment style is of the funds
or at least in this case all the, you know,
equity allocations were driven by random,
the 3-factor model just telling us, you know,
hey how is the performance of our funds related
to the performance of small stocks
or value stocks is what's going reveal by the 3-factor model.
And then ultimately kind
of the takeaway was be careful just simply extrapolating good
past performance of a fund manager into the future,
it can be difficult to differentiate luck from skill.
If you're going to invest
with an active management strategy be comfortable
that you know what the strategy is and ahead
of time why you think it's likely
to be profitable going forward.
