# Some "Portfolio vs Stock Pick" thoughts for the New Year

These are some notes that arose from the key idea that we should cultivate a "portfolio" approach to investing, rather than trying to live or die on the success of each individual stock pick.

For me the conclusions emerged from a understanding the underlying statistics. However the conclusions are also very similar to Stockopedia's "NAPS" approach. NAPS uses a QVM ranking whereas I use a ranking based on Q and the Sharpe Ratio. However the ideas work for any sensible ranking method.

Although I have kept the mathematics out of the main discussion I have included a brief *"Technical Note"* for each section which provides pointers to the underlying mathematics for those who are interested.

The prevailing concept in these notes is that *the portfolio is king*, not the individual stocks within it.

### Technical Note:

There are two key statistical metrics that matter and are discussed here: the **mean return** and the **volatility**. The mean return is often colloquially referred to as *momentum*, or in academic papers it is often called *drift*. It is simply the arithmetic mean of the returns (where a return is the % change over some fixed period, such as daily or monthly.)

Volatility is defined as the standard deviation of the returns. ( = a measure of dispersion about the mean). Volatility is sometimes colloquially called *risk*. Volatility measures how uncertain we are about the returns in the future given what we know about the past.

Sometimes you will read articles which having equated volatility with risk then criticise volatility for "punishing upward deviation" and looking for measures which only count downward (or "harmful") deviation. This is mathematically extremely dubious reasoning. But rather than get into that debate here, just think of volatility as "*uncertainty*" rather than "*risk*".

Important Note: Volatility is computed using returns not prices.

## 1. STOCKS SHOULD COMPETE AGAINST OTHER STOCKS NOT AGAINST THEMSELVES

If you have ever read anything about stock investing, you probably account each stock holding individually. You note its purchase price, watch to see whether it is in profit or loss and then make a decision to sell based on whether it has reached a target profit, or hit a stop-loss. Or you might top-slice to take some profit. The way that your portfolio is reported to you in your broker account will reinforce this. It is traditional to agonise about each decision.

As a result, a stock competes with itself: is it up or down compared with its purchase price? There is no reference to other stocks in the portfolio. Each stock is fighting its own personal battle against its previous price history. We might sell "losers" quickly, but we also sell "winners" so that we can complete the trade and bank a "*realised*" gain. The mindset becomes one in which as soon as a stock is purchased we are constantly asking whether we should sell it or not, and after we sell it, whether that was the right decision. Sometimes the memory of this constant state of anxiety can mean that we dither over whether to buy a particular stock because we know that as soon as it is bought the nagging questions about when to sell will start. This is not a healthy mindset to be in.

This way of working is pervasive in "pop" investing/trading and I rarely see it challenged - so here goes!

Consider a different goal. Instead of choosing *individual *stocks (which we are intending to eventually sell even before we buy them), the aim is to own a *portfolio *with the "best performance" we can achieve and to maintain the portfolio at peak health.

What might "best performance" mean? This is still open to the skill and preferences of the individual investor. "Performance" might be some combination of quality, value or momentum - perhaps chosen using a mechanical screen - or any other method the investor is happy with. But the difference is that the measure of performance is used to rank stocks against other stocks. We choose the highest-ranking (top performing) stocks with the intention of holding onto them - provided that they remain the best of their kind.

The stocks in the portfolio no longer compete with *themselves*; they compete against each other (and the other stocks in the chosen universe of stocks.) If a stock's ranking falls then it is a candidate for replacement by a stock which is performing better. But what about "winning" stocks? Do we sell them to "realise" a gain. Of course not! But we are getting ahead of ourselves - more about portfolio maintenance later. For now we are just trying to build a portfolio - not worry about what might happen in the future.

### Technical Note

If your metric for performance is "momentum" consider using "risk-adjusted momentum" (or high Sharpe ratios) instead. Momentum which is not adjusted for volatility might simply be due to excessive leverage rather than good management or good business. Another way to think about it is that we need to know not only an estimate of how well the stock will perform, but also how much uncertainty there is about that estimate.

High Sharpe ratios correspond to putting your portfolio on the tangent to the "efficient frontier". Below is a plot of the efficient frontier stocks and also some high QVM stocks at 28-Dec-2017. (FXPO here might be the classic example of a high return but *very *high volatility stock.)

2. UNDERSTAND AND EXPLOIT VOLATILITY PROPERTIES WHEN BUILDING A PORTFOLIO

Volatility is just the standard deviation of returns. Although most investors are interested in the percentage gain or loss of a stock, far fewer take an interest in the stock's volatility. However a basic understanding of volatility is very useful and now that Stockopedia quotes yearly volatility for every stock the information is readily to hand.

In a sense volatility is a measure of noise. The movements up and down due to volatility cancel out over the long term but they act to hide the true direction of the stock in the short term.

To see how this works you can use these simple rules of thumb. Imagine a stock with a yearly gain of **Y%** and a yearly volatility of** VOL%**. Then the daily gain will be approximately** d = Y/225** but the daily volatility will be approximately** v = VOL/15 **(note: sqrt(225) = 15). Stockopedia will give both **Y%** and **VOL%** (as "**% Price Chg 1 yr**" and "**1 yr Volatility %**")

Consider a stock with a yearly gain of 90% and yearly volatility of 30%. The yearly gain dominates the volatility (90 > 30) and it is relatively easy to see on a yearly basis which way the stock is moving. But the daily gain is about 0.4% (90/225) with a daily volatility of 2% (30/15). So on a daily basis the volatility significantly dominates the drift and it is very difficult to assess what direction the stock is really moving. When a stock's drift changes, initially you cannot be sure whether there has been a change in direction or whether it is just normal volatility. In addition you should expect a movement of at least **2v** in a single day (either up or down) about once a month.

Another way to visualise volatility is to imagine that a stock with daily gain and volatility (d,v) behaves a rather like a fictitious stock which either moves up by v% or down by v% every day, but the probability that it moves up is ** ½ (1+ ^{d}/_{v}).** So for the earlier example the stock is likely to move up or down by 2% every day with a probability of moving up of 0.5*(1+0.4/2) = 0.6. Over the course of the year the stock will gradually drift up provided that the probability of +2% is greater than the probability of -2% which in this case it is.

These are only crude approximations but they may help to visualise what a given volatility might feel like in practice. 30% yearly volatility is not too bad but 60% is quite a wild ride (expect daily swings of ±4% and more than ±8% in a single day about once a month).

When we combine more than one stock into a portfolio something interesting happens. Because volatility is "noise" some of it cancels out when we combine stocks. Unless the stocks are correlated, the swings caused by volatility occur at different times for each stock. In our simple model above (when we were tossing a biased coin to decide if the stock moves up or down) we toss a separate coin for each stock, so the ups and downs tend to partially cancel and the portfolio volatility can be much less than the volatility of its individual stocks.

This effect will be most pronounced when the stocks have low "*covariance*" and the easy way to ensure this is to make sure that the stocks are well diversified across sectors. But also do not neglect the contribution of the volatility of the stocks themselves. Choosing stocks with lower volatility will also reduce the volatility of the portfolio.

You cannot diversify away all volatility and get a ramrod straight line for your portfolio performance unfortunately. The remaining un-diversifiable volatility is sometimes called "market risk" or "non-diversifiable risk" or "systemic risk" (note how "risk" pops up in these colloquial names). The fact you cannot diversify away all volatility means that in practice by the time your portfolio contains between 10-20 stocks you will have extracted about as much benefit from diversification as you can.

We look for a compromise. If we could choose the one single best stock for the whole year we could put all our eggs in one basket and go with that stock. Because we are not sure about our assessment (and volatility is a measure of that uncertainty) we add more stocks. This will dilute our best performing stocks but it reduces volatility (= uncertainty of outcome). After about 10-20 stocks any benefit from decreasing uncertainty is exhausted so there is no point diluting returns any further.

The effect is surprisingly powerful. A 15-stock diversified portfolio might have a yearly effective volatility of about 5%-10%. This translates into relatively benign drawdowns in normal market conditions. You should ignore the excursions of individual stocks completely. Provided the portfolio as a whole is not suffering a strong drawdown no action needs to be taken on individual stocks (except on fixed intervals - as described next.) A side benefit of low volatility for the portfolio is that it is easier to see whether the portfolio itself has positive or negative drift overall. This can then provide feedback into the quality of your selection rules.

**NB**: when a market crashes, all stocks suddenly manifest highly correlated behaviour and all this cosy talk of volatility and covariance goes out the window. So just because a portfolio has a very low yearly volatility does not mean that you have any protection against a general market crash.

**Warning**: when you include short positions in your portfolio the volatility of the short positions is still added to the volatility of the long positions (although some covariances might be negative). You can't use short positions to reduce portfolio volatility by subtraction. In particular you cannot reduce systemic risk (i.e. hedge) by taking short positions without a lot of calculation. It is dangerous to think that you can. So-called market-neutral portfolios are very technical and tend to be unstable in the sense that they need constant attention to stay neutral. They also occasionally blow up even in the hands of experts.

### Technical Note:

If you know the return for each stock it is easy to compute the return for the portfolio: you just add up the weighted returns of each stock. But to compute the volatility of the portfolio you need to know more than the volatilities of each stock. You also need to know the covariance between every pair of stocks too.

If the stocks all have zero covariance with each other then the square of the portfolio volatility is equal to the sum of the squared weights of the squares of the stock volatilities. So the portfolio volatility would typically be about sqrt(N) (where N = number of stocks in portfolio) smaller than the volatility of the individual stocks. However, the covariance is not zero so the portfolio volatility will not reduce by the full amount in practice. Generally, the more diversified the stocks are the lower the portfolio volatility.

Diversification is just a way to reduce portfolio volatility without maths. But if you can perform *mean-variance optimization* on your portfolio you can avoid explicitly diversifying and let the algorithm simply manipulate the covariance matrix to find the best combination of stocks by itself.

When optimising by algorithm, the way that you specify the problem changes the nature of the solution found. If you optimise for maximal return (so-called growth-optimal or geometric mean maximisation) you end up with about 3-5 stocks. But if you are instead concerned with minimising the risk that a portfolio will return less than some reasonable target return (such as 25% p.a.) then about 10-20 stocks will be the result with a much reduced volatility. My Fantasy Fund is called GOP (for growth-optimal portfolio) but actually it is really closer to a Sharpe-ratio maximising portfolio in practice.

Incidentally, when algorithms build long-short portfolios they generally don't simply go long a bunch of "good" stocks and short a bunch of "bad" stocks. They build a layer cake of alternating long/short through the ranked stocks. The problem is that really bad stocks also have high volatility and you really don't know what they'll do next.

## 3. WHAT WEIGHTING TO USE FOR EACH STOCK IN THE PORTFOLIO

We can optimize the portfolio weightings to maximise the portfolio return and minimise the portfolio volatility. This is the subject of many academic papers about mean-variance optimisation. These algorithms over-weight stocks which are deemed more likely to perform better and under-weight stocks with higher volatility or lower expected returns. However, in practice this is a complicated process which is fraught with problems due to the inaccuracies in the data.

So let's consider two simpler options: market-cap-weighted and equal-weighted portfolios.

The market-cap-weighted portfolio has an interesting property: it never needs to be rebalanced. As the individual stock prices move, their weighting in the portfolio naturally remains correct. This property makes the market-weighted portfolio very stable and is behind the idea of index trackers: portfolios which behave as if they contain the whole market in market-cap-weighted proportions.

However, it has been shown that equal-weight portfolios will tend to out-perform the market-weighted portfolio. They are also easy to compute. Weighting by market cap or by algorithm are best left alone. If you have selected twenty stocks from a market of maybe 1000 stocks, you have already weighted 980 stocks to zero in any case.

### Technical Note

** Modern Portfolio Theory** conjectured that the market-cap-weighted portfolio is the tangent portfolio on the efficient frontier. It removes all idiosyncratic risk leaving just the systemic (non-diversifiable) risk.

A new concept was introduced in

**called the "**

*Stochastic Portfolio Theory**market diversity*" (not diversification) which is an expression of the way that capital is distributed amongst the stocks in a market. Equal-weighted portfolios with rebalancing will out-perform a market-weighted portfolio whenever a market can be shown to be diverse. (Which is "always" for real markets.)

In fact any portfolio which weights smaller-cap stocks higher than they would be in a market-weighted portfolio will tend to out-perform the market-weighted portfolio over the long term according to the theory. Each such portfolio corresponds to a way to measure the entropy/diversity of the market.

There is a curious paradox here. Not all market participants can have equal-weight portfolios. It is mathematically impossible (obviously). And yet for any small investor it is easy to do. Chalk up a cheap win for us.

## 4. REBALANCE OR RE-SELECT ON FIXED INTERVALS TO REMOVE BIAS EFFECTS

So when should you sell individual stocks in the portfolio? In keeping with the idea that stocks should compete against other stocks not themselves, we need a system which sells stocks based on relative performance rather than only considering the stock itself.

This seems to rule out using stop-losses and sell limits which by definition only consider the stock's performance in isolation. Another reason to avoid them is to avoid introducing an unintentional negative edge into the trading activity. A stop-loss is triggered by a negative movement which might simply be the result of noise (volatility) and hence would capture a negative bias. Of course, it may also avoid further moves down.

It is not unusual for even a good stock to lose 20-30% from its peak before recovering and continuing upwards. As we saw earlier, a change in the direction of a stock's drift is indistinguishable from normal volatility in the early stages. So tightly placed stop-losses will cause extra trading costs and in efficient markets will not improve outcomes.

In practice whether a stop-loss works or not depends on many factors. If a market is perfectly efficient stop-losses or any other triggered sell rule will have a neutral bias.

Reassessing your portfolio on a fixed interval basis instead will certainly have a neutral bias as well as being much less mental effort. I have to admit that for me not touching the portfolio between intervals is the hardest rule to stick to. Perhaps I secretly like a bit of mental effort.

Generally, the interval should be between three months and twelve months. At each review, the potential stocks for the portfolio are selected according to the same rules outlined in the first section of this article, and then buys and sells are implemented to bring the portfolio back into line. Usually this will top-slice the highest performers rather than sell them completely. This acts to prevent them dominating the portfolio which would otherwise endanger the benefits of a diversified portfolio.

### Technical Note

Top-slicing high flyers and topping up the laggards will harvest volatility movements even when the market as a whole is not trending but the benefits are quite small compared with choosing stocks with good drift properties.

## 5. PSYCHOLOGY THOUGHTS

This approach is based on mathematics but it seems to have some useful psychological side-effects. It removes the constant pressure to reassess your trades and the guilt of choosing some stocks with poor performance.

In fact you would expect (and you will definitely see) a (nearly) *Normal distribution* of stock returns during the fixed interval. A handful of the stocks will perform dramatically well; a similar handful will perform dramatically badly; and the rest will sit in-between performing fairly averagely.

For example, look at NAPS2017 performance above. (white=median; magenta=mean). A yearly performance of +42% with a volatility of just 8% even though two stocks are down by about 50% and all but one of the stocks in the portfolio have volatilities greater than 20%.

The goal is the portfolio performance will be better than the market index from which you are choosing your stocks, but expect to do that "*on average*" or "*in aggregate*". In other words, if the portfolio out-performs the index then that should be good enough. A few individual stocks which perform badly are normal and to be expected. Think of the portfolio as a "super stock" with good performance and extremely low volatility for a stock.

## 6. SUMMARY

- Don't think of stocks as "winners" or "losers". Concentrate on selecting really good stocks that you would like to hold for a long time unless something better comes along. (Competition between stocks to be admitted to your club.)
- Choose stocks with low volatility and diversify to further reduce volatility of the portfolio. As a consequence, once a stock is in your portfolio it changes what other stocks you will admit. The collection is symbiotic.
- No need to choose more than about 20 stocks
- Rebalance/reselect on a fixed interval. Which stocks will stay in the club?
- Don't beat yourself up continuously about individual trades that go wrong. Instead focus your energy on refining the rules for a stock to join your exclusive club.
- I use this system myself, but I admit that I sometimes break the selling rules.
- Happy New Year!

Filed Under: Portfolio Management,

Disclaimer:

As per our Terms of Use, Stockopedia is a financial news & data site, discussion forum and content aggregator. Our site should be used for educational & informational purposes only. We do not provide investment advice, recommendations or views as to whether an investment or strategy is suited to the investment needs of a specific individual. You should make your own decisions and seek independent professional advice before doing so. The author may own shares in any companies discussed, all opinions are his/her own & are general/impersonal. Remember: Shares can go down as well as up. Past performance is not a guide to future performance & investors may not get back the amount invested.

## 13 Posts on this Thread show/hide all

Nick that is an outstanding post thank you, happy new year

excellent article Nick..

sorry for being cheeky, is there a screen which we can look at the rules.

I need to read multiple times to digest this completely..

Great piece mate..........although I must admit at times I thought I was reading Swahili...........lots to study & understand but really appreciate your time doing this.

An early contender for post of the year.

In reply to tripuram, post #2

Hi tripuram

The stock selection is largely left to the reader to choose. The NAPS system chooses the highest Stock Rank stocks while enforcing a spread of sectors and sizes (and riskiness?) (and I am sure Ed will be along soon with the NAPS 2018 selection.)

If you want a Sharpe Ratio (risk-adjusted momentum) inspired screen, the closest I can get using Stocko screens is something like this:

https://www.stockopedia.com/sc...

I would encourage you to duplicate it and play around with the parameters and add extra screening rules to suit your style rather than adopt it directly. For example, I haven't included a market cap restriction in this version, but usually I avoid stocks with a mkt cap below £100M.

There isn't a way to create a screen to force diversification in Stockpedia. The best you can do is to audit the sectors (or industry groups) and make sure there is no dominant grouping.

In reply to Nick Ray, post #5

Nick - this is a top article. I'll comment properly when I have time... thanks for running the NAPS through the visualisation - is that Matplotlib?

In reply to Edward Croft, post #6

Thanks, Ed.

The analysis is done in R. The efficient frontier plot was produced with ggplot2 and the NAPS 2017 plot was produced with the quantmod library.

Excellent article. Any misunderstanding below is due to limited brain capacity.

This is a bias that I felt strongly and drew me towards more mechanical systems where I don't have to second guess myself.

I've re-read this section a few times and understand the portfolio performance goal. I initially struggled with the selection criteria and just assumed 'relative strength' does this. QVM rankings are attempting to probabilistic-ally select for future positive drift, but if you only care about relative strength ranks, then this could be the basis of creating a pool for subsequent selection from too. You yourself use the Q part with Sharpe. There are many basis for selecting the initial pool of candidates. In fact 'trackers' attempt to do this by selecting from the market pool the fewest shares that replicate the overall market. A different objective but the same principle.

Low volatility and high positive drift (relative strength) is possibly the holy grail for momentum investors who want to use stops but don't actually want them to be triggered. Your explanation of volatility as dispersion around mean return, enhanced my understanding greatly. Thanks.

Time to add volatility to my screens.

Do you know of a source for the R code you've used that can walk an R newbie through this? I've worked my way through R for Data Science and find replicating examples and tweaking accelerate learning. Co-variance matrices are somewhere on the next decades to-do list.

In reply to HumourMe, post #8

I have rather a lot of R code which does many things. But I've put together a very short snippet which would do enough to maybe get you going with covariance matrices anyway. After that, it's up to you! (You could define a function to compute the Sharpe ratio of a portfolio and then use R's 'optim' function to find the portfolio with the highest Sharpe ratio for example.)

The snippet is below (if this 'gist' thing works):

https://gist.github.com/anonymous/af93f187a2a4ffc287011e00c7f133ea

You'll obviously need a copy of R and you will need to install the libraries indicated by the 'require' lines in the snippet. I've tried to keep the code as readable as possible.

Amazing post, thanks for all of the work you put in to it.

In reply to Nick Ray, post #9

thanks Nick.. much appreciated..

In reply to Nick Ray, post #9

Thanks for this. Hopefully I'll be able to start digging into it later this week.

Hi . Your outline helps re-enforce my intention to dump all of my current holdings and then attempt to structure a new portfolio of equal-weighted moat-like stocks . Whilst l have always thought of a portfolio as a " Super Stock " , l have never considered re-balancing the individuals at intervals . Thanks for the inspiration .

Best wishes , Stonor .