On one level, the answer is simple. If an investment reduces your risk, it is a hedge. If it increases your risk, it is a bet. 

So, now it all depends on how you define risk. Also, there is the tricky issue of whether increases in risk are compensated by higher expected return. And this raises the most vexing question of all, namely how to define the relevant portfolio against which the change in risk is measured.  This question is essential to the Volcker rule which holds that banks too big to fail should not be making big bets with house money since the upside would accrue to Wall Street whereas Main Street would have to bail out the banks if it all goes sour. 

In this regard, it matters greatly how you define what constitutes a bet versus a hedge.

Suppose your company can invest $50,000 in return for an even chance of a payoff of $0 or $100,000 (all amounts are stated in net present value terms so that we can ignore the time value of money; let’s also ignore taxes).  Since the expected value of this investment is zero, you either lose your $50,000 investment or have a net gain of $50,000 (i.e., $100,000 - $50,000) with equal chances.  By definition, a risk neutral person would be indifferent, a risk-averse person would reject the bet and a risk taker would accept it. But that is only true if we look at this investment in isolation of other risks in play for this person.  Once we adopt a portfolio view, things get more complicated because the actuarially fair bet above can either increase or decrease the portfolio’s overall risk depending on how its returns correlate with other asset returns in the portfolio.

In the 1950s, Harry Markowitz solved the complex problem of how to optimally balance a portfolio when having to allocate a fixed investment amount across various well-defined securities. Let’s suppose that a risk-averse investor used this basic portfolio model to optimally allocate $1 million across n different investments. Next, assume the investor is given the opportunity to reallocate some of these funds into a new investment offering a negative expected return while also offering strong inverse correlations with many other investments in the portfolio?  Should any funds be diverted into this new (n+1)th security, which on its own would clearly seem to be a risky bet. The answer could well be yes. A risk-averse investor might gladly sacrifice some expected return in the portfolio in order to lower its overall risk. So, paradoxically, what seemed a very risky bet at first suddenly becomes a prudent hedge, or vice versa. 

The question further arises if this dynamic can also happen at a market level, for companies like JP Morgan whose stocks are traded publicly.  The short answer is yes.  The path breaking portfolio work at the individual level subsequently spawned the development of the capital asset pricing model (CAPM) in finance, for which Harry Markowitz and William Sharpe were awarded the Nobel Prize in Economics (shared with Merton Miller). The CAPM examines how rational investors should behave when operating in simplified and idealized efficient markets.  The model showed that investors would only demand an extra return for systematic risk (measured as beta). 

Furthermore, each investor should hold a portfolio comprised of just the risk-free asset and the market portfolio. The assumptions of CAPM have since been relaxed, but its portfolio insight remains, namely that investing in negative return options can be quite rational.  What seems a risky bet in isolation can be a valuable hedge within a portfolio view.  And the reverse can happen as well, as may have occurred at JP Morgan where presumed hedges inadvertently increased risk.

Too little is known yet, in the unfolding JP Morgan scandal, to determine what went wrong at or why. But we do know that:

1. Portfolio thinking can be counter-intuitive.

2. Risk depends on how the relevant portfolio is defined.

3. The devil resides in the correlations among the risks, especially its systemic components.

4. Complex trading strategies can back fire with unintended consequences.

5. Never mistake models for reality since the latter tends to be more unruly than assumed.

6. Sophisticated risk managers are often unduly confident in their models.

7. Those supervising risk managers should never be dazzled by complex math, but ask probing questions using common sense.