Modern portfolio theory can be unintuitive, but an analogy to the insurance industry can make things clearer.
So imagine you are in the business of selling fire insurance policies.
Your long term profits are a function of the premiums you collect minus the claims you pay out.
Your short term risk is the expectation that a given year might have an abnormally high number of claims to pay out.
In this business you have a well-defined risk/reward tradeoff: the total amount of business you will be allowed to do depends on your ability raise capital to survive a really bad year.
Let's look at the risks in more detail.
First of all, some years (like the hot, dry ones) will be bad for the fire insurance market as a whole.
This is "systemic risk", that you can't do anything about.
But in the bad years some policies (like those on wooden houses) will do even worse than average.
You'll probably try to set high enough premiums on these "high beta" policies so that they'll be more profitable, long term, than average;
otherwise, it isn't worth risking your capital base to underwrite them.
Now let's look at what you can do about volatility.
You could ignore volatility, and concentrate only on long term profits.
This is the approach Warren Buffett takes with his ultra-volatile, ultra-profitable "super-catastrophe insurance" business.
Buffett defines his time line as "forever", and cheerfully acknowledges that he will have some truly horrific years with awesome claims to pay out.
Of course he can only do this because he has deep pockets; no matter how bad a year it has, his company has enough capital to survive.
Or you could decrease volatility, through diversification.
For starters, you wouldn't concentrate all your business in one housing development or condominium tower, because the chance of a neighborhood fire would be too great, making your risk of a bad year far worse than the industry average.
So you would spread the policies out geographically, decreasing your risk until it approached the systemic risk of the fire insurance business as a whole.
This is how most people think of diversification, as "not putting all your eggs in one basket."
But you can do even better if you are willing to diversify into other segments of the market.
For example, you'd probably find that the bad years for floods aren't the same as the hot and dry years that are bad for fires.
Diversifying into flood insurance would really let you take advantage of the curved shape of the efficient frontier:
the risk of your diversified fire and flood insurance company would be less than the average of the risks of the two types separately.
So you'd be able to sell more policies, and make more profits.
This analogy seems like a pretty good one, because portfolio theorists think about market returns in the same "random-normal" way that insurance agents think about natural disasters.
Buffett himself doesn't believe in MPT, which is disturbing since he's an expert in both sides of the analogy.
For their part, MPT advocates tend to write Buffett off as a statistical outlier (that means he's a freak from the outer limits of the bell curve) or even as "the exception that proves the rule": out of all the millions of investors in the world you can only identify this one guy - in Omaha, Nebraska for heaven sakes - who seems to be able to beat the market.
But what the MPT crowd should really do is embrace Buffett (something his shareholders would like to do, literally) as proof that their theories work.
Buffett has defined his time horizon; he has established an income source with an unusually well-defined volatility/return tradeoff; he's willing to take concentrated risks if he can survive them and if the reward is great enough... and the results have been spectacular.
Buffett belongs at the center of the bell curve.