Leveraged portfolios will of course have a higher EV if they don’t get margin called. But in an efficient market, the probability of a margin call (and the loss taken when the call hits) offsets the higher EV—otherwise the lender would have a below-market expected return on their loan. Unfortunately most theoretical accounts assume you can get arbitrary amounts of leverage without ever having to worry about margin calls—a lesson I learned the hard way, back in the day.
In general, if leveraged portfolios have higher EV, then we need to have some explanation of why someone is making the loan.
Imagine someone who is extremely risk-averse. They aren’t willing to invest much in equities, but they are willing to make a margin loan with ~0 risk. They will get lower return than if they had invested in equities, and they’ll have less risk. I don’t see what’s contradictory about this.
I was being a bit lazy earlier—when I said “EV”, I was using that as a shorthand for “expected discounted value”, which in hindsight I probably should have made explicit. The discount factor is crucial, because it’s the discount factor which makes risk aversion a thing: marginal dollars are worth more to me in worlds where I have fewer dollars, therefore my discount factor is smaller in those worlds.
The person making the margin loan does accept a lower expected return in exchange for lower risk, but their expected discounted return should be the same as equities—otherwise they’d invest in equities.
(In practice the Volker rule and similar rules can break this argument: if banks aren’t allowed to hold stock, then in-principle there can be arbitrage opportunities which involve borrowing margin from a bank to buy stock. But that is itself an exploitation of an inefficiency, insofar as there aren’t enough people already doing it to wipe out the excess expected discounted returns.)
Imagine someone who is extremely risk-averse. They aren’t willing to invest much in equities, but they are willing to make a margin loan with ~0 risk. They will get lower return than if they had invested in equities, and they’ll have less risk. I don’t see what’s contradictory about this.
Indeed there is nothing contradictory about that.
I was being a bit lazy earlier—when I said “EV”, I was using that as a shorthand for “expected discounted value”, which in hindsight I probably should have made explicit. The discount factor is crucial, because it’s the discount factor which makes risk aversion a thing: marginal dollars are worth more to me in worlds where I have fewer dollars, therefore my discount factor is smaller in those worlds.
The person making the margin loan does accept a lower expected return in exchange for lower risk, but their expected discounted return should be the same as equities—otherwise they’d invest in equities.
(In practice the Volker rule and similar rules can break this argument: if banks aren’t allowed to hold stock, then in-principle there can be arbitrage opportunities which involve borrowing margin from a bank to buy stock. But that is itself an exploitation of an inefficiency, insofar as there aren’t enough people already doing it to wipe out the excess expected discounted returns.)