Return on investment in spreads - Quantitative Finance Stack Exchange most recent 30 from quant.stackexchange.com 2019-05-22T06:43:48Z https://quant.stackexchange.com/feeds/question/32120 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://quant.stackexchange.com/q/32120 1 Return on investment in spreads d--b https://quant.stackexchange.com/users/13640 2017-01-27T10:02:20Z 2017-01-28T16:33:45Z <p>I have a hard time getting my head around this.<br> Let's say you have a strategy that consists in buying one future spread, for instance CL Z7-Z8 (crude oil dec17 minus dec18). It's easy to calculate the PnL of that strategy:</p> <pre><code>PnL = quantity * lot_size * (spread(t) - spread(0)) </code></pre> <p>where spread(t) is the spread at time t and spread(0) is the level at which you entered.</p> <p>Now, to calculate the return of that strategy, you'd have to assume that this corresponds to a certain capital that's at risk.</p> <pre><code>Return = PnL / InvestedCapital </code></pre> <p>Given that entering the future spread will demand an initial margin call, and subsequent maintenance margins (potentially infinite), how does one "assign" a capital to that strategy?</p> <p>Is it just a matter of choice? Can tell myself: I'm committing 100k to that strategy, and with that I can buy the amount of spreads that I think will not make me go bust, which I'm assessing corresponds to 10k of initial margin calls?</p> <p>But if that's the case then I could just as well commit 200k, and buy the same 10k of margin calls, which means I would be half as leveraged.</p> <p>Is there a usual way of doing this? For instance where we say that the capital that's at risk is the amount you would loose if the spreads goes 7 stddevs out, or something like that?</p> <p>Sorry if I'm not being very clear, it's kind of messy in my head right now...</p> https://quant.stackexchange.com/questions/32120/-/32128#32128 2 Answer by Chris Taylor for Return on investment in spreads Chris Taylor https://quant.stackexchange.com/users/924 2017-01-27T16:08:03Z 2017-01-27T16:08:03Z <p>What is the return on a strategy which has no up-front cost to implement? I argue that it doesn't really make sense, and that the most sensible approach is to define a 'trading capital' that you are comfortable with, and measure returns against that.</p> <p>In fact, to come up against this problem you don't even need to think about spread strategies. You might see the return on a futures contract priced at $F_t$ defined as</p> <p>$$R_{t+1} = \frac{F_{t+1} - F_t}{F_t}$$</p> <p>but this is misleading, since it is zero cost to enter a futures contract (if you ignore initial margin). The quantity $F_t$ that you are measuring return against is the notional contract size, but it has no relation to the amount of capital required to run the strategy.</p> <p>Compare it to the return on a cash equities position with price $P_t$ and dividend $D_t$,</p> <p>$$R_{t+1} = \frac{P_{t+1} + D_{t+1} - P_t}{P_t}$$</p> <p>Here it makes sense that the denominator is $P_t$ since this is the capital outlay required to buy the stock at time $t$.</p> <p>If you want to think in terms of return rather than profit and loss, I would define a nominal 'trading capital' $X_t$ for the strategy, and measure returns against that,</p> <p>$$R_{t+1} = \frac{\textrm{PnL}_{t+1}}{X_t}$$</p> <p>You can choose whatever value of $X_t$ you are comfortable with. A common approach is to choose $X_t$ so that the annualized standard deviation of returns is some acceptable number (5%, 10%, 15% etc) or to choose it so that a certain sized drawdown (say \$10k) would result in a loss of a specific percentage of your capital (e.g. if you wanted a$10k drawdown to correspond to a 10% loss of capital, you choose your initial capital to be \$100k).</p> <p>As you say, you can choose your initial capital to be \$200k and size your positions exactly the same way as if you had committed \\$100k, in which case you have half the risk (i.e. volatility is halved, drawdowns are halved etc).</p> <p>As a general piece of advice, it is probably sensible risk management to actually hold your trading capital, whatever amount it is, in a money market account (or somewhere else safe) so that you earn a risk-free return on it, and you can use it to meet margin calls when they become necessary.</p>