In this very complex and volatile environment, the aversion to sell out of a losing position is a very powerful instinct. In trading we do not seem to view a paper loss as real until it has been crystallized, so we tend to postpone the painful feeling of losing money. We are also reluctant to admit that we made a mistake with our initial trade. Selling is an admission of failure. Conversely, if a position has risen in value, we are happy to take profits and sell quickly. The main motivation behind selling positions at a small profit appears to be to minimize regret. If NVIDIA, for example, fell back after reaching a new high, we would castigate ourselves for not taking profits earlier. Selling also confirms that our initial buy decision was correct. We hunger to get the confirmation as quickly as possible. Both of these effects are at odds with classical financial theory, which says that people’s actions and preferences for risk are unrelated to whether they have made paper profits or losses. In contrast, we take more risks in a losing position to get even, but we want less risk when winning, preferring a quick and certain gain to a chance of losing our profits. Fortunately, there is a solution. The answer is to fully, or partly, systematize our financial decision making. This will give us the best of both worlds – our human ability to interpret and process information, combined with a system giving the correct amount of risk.
As discretionary traders, we trade sporadically as opportunities arise. At any given time, we have a small number of positions or bets open. Those positions are drawn from a larger pool of opportunities that we have formed opinions on1. Each time we enter a new bet we make a forecast either on gut feeling or using analysis which cannot be systematized2.
This presents a problem because the make-up of our portfolio, and hence the correlation of returns, will change over time as different instruments come in and out. The simplest thing to do is to limit the maximum number of bets that can be placed at any time3. But to ensure the risk is properly controlled we will be using a trailing stop loss rule to close all our positions - no other exit rules are permitted4. This means the average holding period will depend mainly on how tight, or loose, the stops are set. If stops are set very tight, then we will have short holding periods and high turnover. We should then ensure that our trades and the horizon we are trying to predict price movements for, is in line with the trailing stop levels.
Sticking to this position management process will be difficult. It will force us to close positions to keep the amount of capital at risk constant, or prevent us from trading, when we would rather do otherwise. If we already have our maximum number of bets on, and we desperately need to make a new bet, then sorry: we cannot. Wait until one of our existing bets has stopped out. If they all continue to be profitable then perhaps our new bet was not necessary after all. Although this may seem rigid, it ensures that we have the correct risk on for each bet, and it will stop us from putting on dangerous numbers of simultaneous bets.
There are substantial advantages to using discretionary forecasts with stop losses; we can make predictions about the behaviour of our live trading and measure expected risk more precisely. Our positions will always be the correct size for a given forecast, tolerance for risk, and account size. This will give us more time and energy to get the forecast right. But once a bet is open, we should not change the forecast. Otherwise, there is the risk of meddling, taking profits too early by reducing the conviction of our forecast or doubling up on a loss. We could sometimes add to positions by placing a new, separate, bet on an instrument which we are already holding. This allows pyramiding positions, such as buying into a strengthening trend. But a new bet on an existing position also counts towards our maximum number of bets. The new bet is completely distinct, will have its own stop loss, and could be closed at a different time.
Lastly, by using a systematic trailing stop loss rule to close all our positions we would be trading somewhat like an ‘early loss taking’ trend follower, so it’s more likely our P&L will have a benign positive skew. I am a big fan of trend following rules. Firstly, they work. There is a lot of academic research and real performance statistics supporting it. Secondly, we like rules that will close positions that have started to lose money. We may hit stop losses more frequently, but when trends occur it will exploit them. This is also how the ‘early loss taker’ behaves. Also, trend following is an easy to implement trading strategy using only pricing data. And finally, it has made mincemeat of its opposition, the negative skew trades, small consistent gains until the trade goes terribly wrong. These steady gains tricked us into thinking that the position was low risk and lured us into using leverage to improve our returns. But we have the unpredictable risk that the volatility or correlations will change, and for negative skew positions it will usually surprise with large losses rather than gains. So, beware of gearing up on apparently low risk with an asset or with a style of trading which is likely to have negative skew, even if we have not yet seen any evidence of the large downside5.
With the systematic position management framework there is a series of calculations to be performed each time we trade. To reduce the workload, we first need some daily housekeeping: closing out any positions that have hit stop losses, adjusting estimates of trading capital and price volatility, and doing any trades on existing positions that are now required. We will then put on any new trades which look promising based on overnight moves. We will continue to watch the markets, potentially putting further trades on, and closing positions that hit stop losses.
Check stops: If not using stop orders left with brokers check to see if any stop levels have been hit on existing positions, and if necessary do closing trades.
Get account value: Get today’s account value and calculate your current trading capital. Your annualized cash volatility target is current capital \(\times \text{ percentage volatility target}\) (in this example I use \(90\%\)).
Daily cash volatility target: Daily cash volatility target equals one-sixteenth of annualized cash volatility target. (As usual this is the ‘square root of time’ rule; with around \(256\) trading days in a year we should divide by \(16\) to go from annual to daily risk.)
Get latest prices: Get charts for all stocks we have positions on and ideally anything we might wish to trade today.
Calculate daily price volatility: Using a one month chart eyeball the price volatility of each instrument we own, or might trade today. With FX rate of \(USD\$1\) and relevant block values convert this to instrument value volatility. For existing positions if the volatility level we used yesterday is not within \(25\%\) of today’s level then update our estimate; otherwise stick with yesterday’s estimate. For potential positions we should always use the most up-to-date estimate.
Recalculate stops: Update stops on existing instruments so they trail new highs (for longs) or new lows (for shorts), and account for the latest value of price volatility.
Volatility scalar: This is equal to the daily cash volatility target divided by the instrument value volatility for each instrument.
Desired subsystem position on an existing bet: Original forecast multiplied by volatility scalar, divided by \(10\).
Desired portfolio instrument position on an existing bet: Desired subsystem position multiplied by instrument weight and by instrument diversification multiplier. With the maximum of \(8\) bets use in the example, and an average of \(5\) bets, we should use an instrument weight of \(12.5\%\) and a multiplier of \(1.6\).
Desired target position on an existing bet: Portfolio instrument position rounded to nearest whole block.
Issue trades on existing positions: Compare current position to target position. If out by more than \(90\%\) then issue adjusting orders (position inertia).
Check setups: Check charts and news for potential new bets. If any exist go to instructions for new position opening.
Calculate forecast: Weighted average from the IC meetings.
Is it allowed?: Do we already have the maximum number of bets on? (For this example is \(8\).) Is the bet on an instrument with an existing position? If so it must not reduce or reverse the position.
Calculate instrument value volatility: If not pre-calculated in the morning, using a one month chart eyeball the price volatility of each instrument. With \(FX\) rate of \(USD\$1\) and relevant block values convert this to instrument value volatility.
Calculate stop loss: Use \(X\) multiplied by the daily price volatility in price points to find where to set the stop loss relative to the entry price. For this example I use an \(X\) of \(8\).
Volatility scalar: This morning’s daily cash volatility target divided by instrument value volatility for the instrument.
Subsystem position: Forecast multiplied by volatility scalar, divided by \(10\).
Portfolio instrument position: Subsystem position multiplied by instrument weight (\(12.5\%\) in the example) and then multiplied by instrument diversification multiplier (\(1.6\) in this example).
Rounded target position: Portfolio instrument position rounded to nearest block.
Trade: We should now put on the trade and once completed calculate the initial stop loss relative to the entry price. With judicious use of programming the above steps can be completed in a few moments.
I strongly recommend not to deviate from this position management process. It wont guarantee vast outperformance, but it will make failure less likely. Success in the money management business is mostly down to avoiding common mistakes such as over complicating financial decision making, being too optimistic about likely returns, taking excessive risks, and trading too often.
As discretionary traders we have a graduated opinion on likely price movements whenever we decide to open a new position or ‘bet’. These need to be translated into quantifiable forecasts.
We will be measuring our trading capital daily, recalculating volatility target, and adjusting stops accordingly. This might trigger trades on existing positions and the new volatility target will be used to size any new bets we make. As suggested, we do not need to update the volatility estimate unless it has changed by more than \(25\%\) from the previous value.
The stop loss rule set stops at a multiple (\(X\)6) of the current value of the daily standard deviation of prices:
Trailing stop loss when long: If the price of NVIDIA, for example, falls by more than X volatility units from the high achieved since entry then we should close the position. As an example suppose the high of NVIDIA was \(\$300\), so with \(X=8\) and volatility units of \(\$12\), that implies a stop loss of \(\$300 - (8 \times \$12)=\$204\)
Trailing stop loss when short: We will generate a closing trade when a price rises by more than \(X\) volatility units from the low reached after entry. So again for NVIDIA if the recent low was \(\$250\), then that implies a stop loss of \(\$250 + (8 \times \$12)=\$346\).
The use of systematic stop losses allows to compare this framework with traditional money management systems, where we put a fixed percentage of capital at risk. The different characteristics of positive and negative skew strategies determine our likely appetite for risk. It is possible to infer the percentage volatility target that is implied for a particular trading system if we know the approximate holding period, the average number of positions held and the maximum amount of capital put at risk on each trade.
Readers may be interested in our NVIDIA Valuation Presentation FY2017-2023, a behemoth weighing in at \(174\) slides, that sheds insight into our thinking, investment philosophy, conviction, and much more: https://www.linkedin.com/pulse/nvidia-valuation-presentation-rafael-nicolas-fermin-cota/↩︎
There are a small number of investors who seem to be able to persistently generate extraordinary profits (e.g., Warren Buffett) that none of the above theories can easily explain. It is possible they are just very lucky, the one in a billion monkey who has by sheer fluke successfully written a sonnet. But they may possess the rare elixir of alpha; genuine skill in making investment decisions. It is unlikely that what these outliers do can be written down and reproduced systematically. Those who exhibit pure skill can adapt to changing market opportunities in a way that a systematic rule never could.↩︎
For example, if the notional maximum number is \(8\) bets this implies each stock weight will be \(100\%\) divided by \(8\), which equals \(12.5\%\) for each instrument. I also recommend that this maximum should not be more than \(2.5\) times the average number of bets we expect to be holding over time. The stock diversification multiplier should be our maximum numbers of bets divided by the average number of bets. So, if we had an average of \(5\) bets on at any given time, with a maximum of \(8\), then our multiplier would be \(8 \div 5 = 1.6\). As I said this means it is advisable that the maximum number of bets is not more than \(2.5\) times the expected average, since if we end up frequently trading more than our average then our expected risk will be too high. This essentially assumes that all bets are always highly correlated, which is very conservative. Here is the proof of this result. Suppose we are aiming for a daily volatility target of \(\$1,000,000\) and have an average of \(5\) bets, with a maximum of \(8\). All portfolio weights are \(100\% \div 8 = 12.5\%\). Each trading subsystem will also have a volatility target of \(\$1,000,000\). Once multiplied by the portfolio weight each subsystem position will have an average volatility of \(\$125,000\). On average with \(5\) bets, all of which are perfectly correlated, our daily portfolio returns will be \(5 \times \$125,000 = \$625,000\). So to hit the overall target of \(\$1,000,000\) we need a diversification multiplier of \(\$1,000,000 \div \$625,000 = 1.6\).↩︎
There are some situations where closing trades before a stop loss is hit makes sense, such as relative value or mean reverting strategies, but in my opinion, it is much better to build the closing rule into a fully systematic rule. For example, relative value strategies which need high leverage are particularly vulnerable to crowds. Often after a long stable period of rising markets these trades get swamped by people seeking extra returns. This results in the available profits being reduced, the apparent risk falling, and required leverage increasing further. Then the music stops, and their negative skew becomes horribly apparent. Two classic examples are the meltdown of fixed income relative value hedge fund manager Long Term Capital Management in mid-\(1998\) and the Quant Quake - sharp losses seen over just two days by equity relative value systematic funds in August \(2007\).↩︎
Readers may assume that I have strong dislike for certain investing styles and instruments, in particular those with negative skew. Nothing could be further from the truth, and I am firmly against trading instruments or strategy with very low volatility and leveraging up negative skew trading rules too highly. Holding very low volatility assets is generally a bad idea, and this is yet another reason to avoid them.↩︎
Parameter \(X\) is
related to how long we want to hold positions for and our trading costs.
\(X\) is equivalent to the \(B\) parameter in the generic
A and B system which I describe in
https://rpubs.com/rafael_nicolas/early_loss_profit_takers.↩︎