Leverage

Foreword

This post discusses leverage, a tool to magnify the profits (or losses!) from your portfolio. Think of leverage as a tool — you can use it to ramp up the risk you are taking in your portfolio, or tamp down the risk (by reducing leverage). In that sense, leverage provides a lot of power to the investor or speculator to fine tune their exposure to the market.

But remember — with great power, comes great responsibility.

As usual, a reminder that I am not a financial professional by training — I am a software engineer by training, and by trade. The following is based on my personal understanding, which is gained through self-study and working in finance for a few years.

If you find anything that you feel is incorrect, please feel free to leave a comment, and discuss your thoughts.

Definition

First off, let’s clarify what I mean by “leverage”.  Typically, leverage means you borrow money, or via some other means, put a multiplicative effect on your capital, such that potential gains or losses are magnified as well.  For example, borrowing $100 on top of your existing $100, to buy $200 worth of stocks, or buying options, trading futures, etc.

I generally quantity leverage as a continuum between 0 to infinity, where a leverage of 0x means you’re in 100% cash, and a leverage of Nx means for every 1% move of the asset (some people use “market”, defined as S&P 500 index), your portfolio value moves by N%. For example, if you have a portfolio of $100, of which $50 is in SPY, then your leverage ratio is $50 / $100 = 0.5x.

Next, I’d like to discuss a term I invented — “holding power”.  Essentially, think of this as a mix of psychological and financial wherewithal to hold on to a position.  If you have $100 to your name, and you need that $100 to buy food for tonight, then you have very low holding power — you desperately need that money to survive, so you are not financially capable of losing that money.  If you have $1m to your name, but you really cannot stand the thought of losing money, you too have very low holding power — even though you can afford the loss financially, you are not psychologically prepared for it.

Why is leverage important?

The term “Sharpe Ratio” gets thrown around a lot.  Implicitly, a higher “Sharpe Ratio” is generally taken to be a good thing — it means your strategy is more likely to make money.  But does it really?

The Sharpe Ratio is just the ratio of the expected returns over the standard deviation of returns (1).  The layman way of thinking about it is:
Your portfolio doesn’t return the same amount everyday.
You can think of it as, your portfolio returns R, with some “noise”, N, for a daily return of R + N(day),
where R is a constant (the expected return) and N(day) can be expressed via the standard deviation of daily returns.

Sharpe Ratio = R/N then, gives you an idea of how your expected return compares, against “random noise” in daily returns.
Higher = more signal = less noise = better.

One of the first uses of Sharpe Ratio, is for portfolio planning.  The intuition is simple — If you have a strategy that is high Sharpe, then you can put more money (i.e: more leverage) into that strategy.  Because a strategy with Sharpe >1 has a low (2) chance of losses on a daily basis (or whatever period you use to calculate your Sharpe Ratio), you can worry less about a margin call (more on this later).

In other words: higher Sharpe Ratio = more “holding power”.

In CAPM and MPT, one of the core assumptions/results is that you leverage more (i.e: put more money into) assets with higher Sharpe Ratio’s. So, if you are discussing CAPM, MPT or Sharpe Ratio, but you are steadfastly against leverage, then it’s… kinda weird?

Margin loan

A margin loan is a direct loan you take out from your broker to buy stocks.  For example, if you deposit $100 into your brokerage account, and you buy $150 worth of stocks, you have $100 in equity and $50 on margin, and your leverage ratio is ($100 + $50) / $100 = 1.5x.

Typically, brokers use Reg-T (this is the name of the SEC rule) to determine how much margin you can have.  The math is complicated and has a lot of corner cases, but essentially, you are required to have ~50% equity (i.e: 2x leverage) when you open new positions.  IIRC, maintenance margin is 25%, which means at any time, you must have at least 25% equity (i.e: 4x leverage).

If you fail either of these 2 tests, your broker will issue a margin call to demand that you put in additional equity (usually via wiring more money).  Some brokers give you 1-2days to send in the money, others give you (literally) 5-10minutes… or less.  If you fail to meet your margin call, your broker has every right to force close your positions (i.e: close your positions) until you meet the requirements.  In some cases, the broker can force close more than is absolutely necessary to meet the 2 tests, e.g: get your maintenance margin to 50% or even higher. Some brokers may even force close your positions without issuing a margin call.

In other words:

• Margin loans lowers your financial holding power.
• More leverage lowers your psychological holding power.

Some brokers offer what is known as “portfolio margin”.  This is a case by case basis, and each broker implements it slightly differently, but essentially allows you more leverage than the 50%/25% of Reg-T. They do this by analyzing your portfolio, and if they deem it low risk, they can extend you more leverage.

Now, consider a margin loan — you put in $100, you buy $100 worth of StockA and $100 of StockB.  Is your loan to buy StockA or StockB?
The answer is, neither, and both.

Instead of thinking about “getting a $100 loan to buy Stock?”, you should think of it this way:

• You have assets of $200.
• You have debt of $100 (the margin loan).
• You thus have equity of $200 – $100 = $100.

Effectively, you are giving the broker $100 (cash) to maintain a position of $200 of assets. Whether the broker used your actual $100 to buy the stocks, or put your $100 in a little box and then used their own $200 to buy the stocks, doesn’t really matter. The $100 you put in, is the collateral for the broker.

Any losses to the $200 of assets, first comes out of that collateral.  If the collateral is depleted, then the broker may start losing money — because the asset is now worth less than the loan, unless the broker can force you to cough up the difference, they’ll have to eat the loss.

Therefore, the broker will generally force you to put in more collateral (margin call), or force reduce your position (so they cannot drop in value even further), way before your equity reaches $0.

If you think of it this way (using collateral), then it’ll be easier to reason about why you need to put money in when you are shorting stocks (and thus getting cash from selling the stocks) — you aren’t putting money in to sell stocks, you are putting collateral in to support your position of “short stocks”.

Futures

You can also get leverage by trading futures.  A future contract is essentially a standardized forward contract — Forward contracts cannot be traded on exchanges, they are just bespoke contracts any 2 entities write to each other to transact at a future time.  A future contract has standardized terms, so the contract itself can be traded.

I won’t go into details of a future contract, but the gist is:

• To open a position (long or short) in a future contract, you need to put in collateral.
• If you buy 1 contract of MES, you are agreeing to buy 5x<S&P500 value> at the expiry.
• To make sure you can cover 5x<S&P500 value>, the exchange may require collateral of (I can’t remember exact value, this is completely made up) $100.
  • i.e: $100 of collateral, lets you control ~15k worth of future trade value.  Hence leverage.
• Like margin loans, futures subject you to margin calls.
• Unlike margin loans, futures usually allow you to get much higher leverage ratios.

Most types of leveraged ETPs (3) are actually implemented on the side of the fund provider as futures. In other words, for every share of a leveraged ETP, the fund provider just buys some futures on behalf of the ETP owner.

In effect, leveraged ETPs can be thought of as futures, but packaged in such a way that prevents you from getting margin calls. This is not always a good thing! In exchange for not getting margin called, the leveraged ETPs stand a chance of losing a large portion, including 100%, of their value very quickly. In some sense, margin calls tend to protect against a 100% loss (because the broker will usually force close your positions before you even get close).

Options

Options are the last form of leverage commonly available to retail traders.  An option contract is basically a standardized warrant contract, i.e: forward to future, is the same as warrant to option.

Buying an option contract gives you the right, but not the obligation, to buy (call) or sell (put) 1 lot (usually 100 shares) of the underlying stock at expiry, at a certain price (strike price). The seller of the option is at the mercy of the buyer — the buyer decides whether and when to exercise the option and force the trade in the underlying.

Depending on expiry date and strike price, the cost of the option contract changes.  It is possible, though rarely profitable, to get 100x or even more leverage with options.

Brokers are not allowed to let anyone buy options on margin. Therefore, if you buy an option contract, the maximum amount of money you can lose, is the amount of money you spent buying the contract.

Therefore, being long option contracts doesn’t lower your financial holding power.  However, they may still lower your holding power overall, because options are still leverage, and that can lower your psychological holding power.

Cost of leverage

Now, how much should a broker charge for a margin loan?  How much should the exchange demand in collateral for a futures contract?  How much should an option contract cost?

The answer to all these is basically dependent on 2 things:

1. Volatility
2. Prime rate (or risk free rate, since they are related)

Margin loans

How much margin you are allowed (the 50%/25% bits) is actually modified by the volatility of the asset you are buying.  Some assets are rated at 100% (e.g: $1 in ICSH is worth $1 of equity).  But some assets are rated at less (e.g: $1 in GME is worth less than $1 of equity in Jan 2021), because those assets are too volatile.

So, volatility affects your maximum leverage. More importantly, remember that volatility of an asset can change at any time, so your maximum leverage can change at any time.

At the same time, the actual cost of the margin loan is typically fixed at some offset from prime rate, e.g: your broker may charge you 8% over prime, which means prime rate + 8% on an annualized basis, for every dollar of margin loan.

Margin loans tend to be very expensive, regardless of volatility.

Futures

Futures pricing is complicated, but essentially takes into account prime rate — otherwise you can arbitrage by buying a future, shorting the stock, and investing the net cash in safe assets like Treasuries.

In general, futures cost more as prime rate goes up. However, because prime rate is generally low (0-1%) pretty much since 2009, the cost of leverage using futures is “cheap”.

At the same time, if the asset is volatile, the bid/ask spread of the future contracts may be larger.  So while the midpoint of the future contract may remain static, it can still cost you more to trade futures if volatility is high (via crossing the spread).

Options

Like futures, options are priced off prime rate.

However, because options are not symmetric (unlike futures, where both sides must trade, options give one side the right to decide whether to trade), the price of options tend to go up when volatility goes up.

Essentially — the more likely the stock price moves (higher volatility), the more you should expect to make money off the option contract, and thus the more the contract should cost.

In general, futures are the cheapest form of leverage, followed by options, followed by margin loans.

Why is holding power important?

The market doesn’t go up or down in a straight line.  Even if the market will definitely be higher tomorrow, from now till tomorrow, it can still go down.

Having more holding power allows you to wait through the ups and downs of your portfolio, and, assuming your thesis is correct, avoid you being forced to close your position before you can realize your profits.

In particular, remember that margin loans and futures give someone else the right to force close your position, if you are in breach of your contract (futures contract or margin loan contract).  This means that you need to build more buffer in, effectively reducing your leverage.

Why is any of this important?

Because you can potentially save money, and/or increase your holding power (and thus more likely to profit) if you structure your portfolio’s leverage properly.

For example, if you have $100, and you want to buy 100 shares of a stock worth $2 each, $200 total, it may be cheaper to do:

1. Sell 1 put at strike $2
2. Buy 1 call at strike $2

At expiry, if the stock is below $2, the buyer of the put will force you to buy 1 lot (100 shares) of the stock at $2 each.  If the stock is above $2, you can exercise the long call to buy the 100 shares at $2 each.

To support the short put, you need to have enough equity to support holding100 shares.  However, because you aren’t actually buying the shares, you don’t pay for the margin loan — you just need enough cash in your account to support that hypothetical position. If you have margin enabled on your account, this amount of cash can be substantially less than $2 * 100 = $200 — it’s likely around $100, reflecting 2x Reg-T margin requirements.

Also, when you sell the put, you get some money, which you can then use to offset (perhaps completely!) the cost of the call.

In the end, you need roughly the same amount of equity to support this synthetic long position.  At the same time, the pricing of both call and put will be reflective of the current spot price of the stock, adjusted for volatility and prime rate.

So you “pay” for volatility when you buy the call, but you also “sell” volatility when you sell the put, so your net price is relatively immune from volatility changes.  You do, however, pay for the leverage via prime rate (it’s complicated), i.e: your cost of leverage is roughly prime rate, which is a lot cheaper than the typical retail brokerage margin loan rates of prime + 6-10%!

Note: The short put means that you are obliged to buy the stock if it falls under $2.  This effectively means that if your equity falls too low, your broker can margin call you.  Unlike being long options, when you are short options you are subject to margin calls.

There are a lot of different ways you can structure your leverage to reduce cost of loan, and/or to increase your leverage without dramatically decreasing financial holding power (e.g: by doing it in a way that doesn’t allow your broker or the exchange to margin call you).

In practice, I very rarely use margin loans — instead, I typically use futures or options instead when I want leverage.

Footnotes

1. Not exactly — it’s actually the expected excess returns over standard deviation of excess returns.   For simplicity, however, many people just ignore the risk free rate.  This becomes even easier to ignore after 2009, where RFR is almost 0% most of the time.
2. I believe 5%?  I don’t know, I’m really bad at statistics.
3. ETP stands for exchange traded products, which is a generic name for both ETF (exchange traded fund) and ETN (exchange traded note), combined.