Modern Portfolio Theory: Asset or Liability? Part I

  • What is MPT, and why is it important?
  • What are MPT’s assumptions, and are they correct?
  • Is there a better way to invest?

And over the hump, we go.

It’s a fine Wednesday here in Cebu.

I’ve got to drop off my mother-in-law at the pier so she can take her boat back to Samar.  Samar is another island in the Philippine Archipelago where she lives, and Pam grew up.

It’s great to have family around the house.  It’s almost a luxury for us!

Going through the mailbag, I found another request that lit me up.  Honestly, I don’t know how I didn’t write about this before.

But thank you to Ed Kelly for nudging me into action!

A Little Background to the Background

As you know, every summer, I teach recent college and MBA graduates who are entering banks.

It’s my job to teach total newbies about the financial markets.  It’s also my job to get the business majors, well, less theoretical and more practical.

You can probably tell that no one loves the sound of my voice more than I do.  That’s why this will be my sixteenth summer teaching.

I can’t believe how fast it’s gone since March 2007, when I first started.

One of the critical areas for the kids – yes, they’re kids, and the darn things keep getting younger! – to learn is portfolio theory.

As banks are the “sell-side,” their clients are usually from the “buy-side.”

The buy-side consists of asset managers and hedge funds, who serve the “real money” clients.

Real money is the term we use to describe fully-funded, long-only asset managers and their clients: pension funds, sovereign wealth funds, insurance companies, and endowment funds.

That is, they have “real money” to invest and are not levered like hedge funds.

So, to know their clients, young bankers must learn what real money – or institutional investors, as they’re sometimes called – do with all the cash they have.

Modern Portfolio Theory: Background

One of the problems presented to fund managers is simple: what do we do with all this money?

In 1952, a young economist named Harry Markowitz wrote a paper called Portfolio Selection.  It was published in The Journal of Finance, Vol. 7, No. 1 (Mar. 1952), on pages 77-91.

Markowitz studied at the University of Chicago under Milton Friedman.

In 1959, Markowitz published Portfolio Selection in expanded book form at the invitation of James Tobin, an eventual Nobel Prize-winning economist.

The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1990 was awarded jointly to Markowitz, along with Merton H. Miller and William F. Sharpe “for their pioneering work in the theory of financial economics.”

So one thing’s for sure: the theorists and prize winners love Modern Portfolio Theory.  (That’s the name colloquially used to describe Markowitz’s entire body of work.)

The Purpose of Modern Portfolio Theory

I’m going to write as if I’m next to you with my coffee.  So I’ll avoid jargon as much as I can.

The purpose of MPT is to maximize an investor’s returns for his given level of risk.

Markowitz confirmed that a portfolio’s return is the weighted average of the returns of the individual securities in a portfolio.

That is if stock A had an expected return of 2% and stock B had an expected return of 10%, the portfolio’s expected return would be (50% x 2%) + (50% x 10%) = 6%.

But Markowitz discovered that portfolio risk isn’t just a weighted average of the individual risks of the stocks.  You had to take the correlation between the two stocks into account.

Without getting all mathy on you, let me visually demonstrate what happens with a portfolio of two stocks.

In our little sandbox, stock A has that 2% expected return and a 5% standard deviation.  Stock B has that same 10% return with a 12% standard deviation.

They are the only two stocks we can invest in.

In finance, the standard deviation is synonymous with risk and volatility.  This is based on a normal distribution or bell curve, and I’ll explain this more tomorrow.

I will vary the correlation between the two stocks to show you how important it is.

In our first screenshot, both stocks are perfectly positively correlated.  That is, they move in lockstep with each other.

If we’ve got a 50/50 portfolio, the expected return is 6%, the portfolio standard deviation is 8.5% (the average of the two stocks’ risks), and the minimum standard deviation we can achieve with this portfolio is putting 100% of our money in stock A, which has that 5% risk.

Then, it’s not much of a portfolio, is it?

What happens when there’s no correlation between the two stocks?  That is, we can’t see a relationship between the movements of the two stocks at all.

What’s interesting about this is how the line is now a curve.  If we stick with our 50/50 mix, we have a portfolio with the same expected return of 6% but an expected risk of 6.50%.

We lowered our risk by 2.00%, just by having assets that now did not correlate.

And if we wanted to minimize risk, we no longer had to put all our money in stock A.  We would put 85% in stock A and 15% in stock B to achieve an expected portfolio risk of 4.62%.

That’s a much lower risk than when the stocks are perfectly positively correlated.

Let’s do one last example.

Let’s now make our stocks negatively correlated with each other.  We won’t do a perfect negative correlation.  Let’s make the correlation -0.70.

What happens?

With a -0.70 correlation, for our 50/50 portfolio, we have an expected return of 6% still but a risk of only 4.61%.  That’s a pretty dramatic reduction from 6.50%.

But our minimum variance portfolio – the one with the lowest risk – only has a risk of 2.69%.  We achieve that by putting 74% of our money in stock A and 26% in stock B.

To be sure, the entire curve is called the “minimum variance frontier.”  The “efficient frontier” is the “top side of the bullet.”

That is, only those portfolios with a higher risk and a higher return than the minimum variance portfolio are what we’d call efficient.

That means they earn the highest return for a given level of risk.

Part I Wrap Up

As we’re already over 1,000 words, I’ll save the assumptions of MPT and its (valid) criticisms for tomorrow.

But I assure you that if you grok what I’ve written above, you probably understand this stuff better than the graduates I teach at the top US banks.

Does all this stuff actually work?

Well, yes and no.

Does it give a theoretical foundation to everything we do?

Yes, unequivocally.

Do the outcomes usually reflect the analysis?

You must be joking.  That’s a big, fat NO.

Let’s have fun with this tomorrow.

All the best,

Sean

 

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