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Apocalypse-now insurance
Nassim Nicholas Taleb, the options trader turned polymath who introduced the financial world to the apocalyptic potential of black swans, is in no doubt at all – insurance for an equity portfolio is a must. “No insurance, no portfolio,” is his epithet on the matter.

For Mr Taleb, the analogy is with household insurance – it’s something you buy regardless of its price and regardless of the timing. It is simply a cost that goes with home ownership, just as surely as the cost of heating and lighting, because not to have property insurance would be bonkers. So it is with an equity portfolio – the cost of insurance is much the same as the cost of a broker’s commission or a market maker’s spread. It is a price of being in the game; it is the one you pay to emerge relatively unscathed from the worst the market can throw at you. 

History seems to be on Mr Taleb’s side. No sooner had the 2008-09 financial crisis delivered a shock to equities that should only come around once every 1,000 years (and certainly not just eight years after the high-tech bubble burst) than up popped Covid-19, another one-in-1,000 event. Granted, the Covid-19 shock was not a black swan event, says Mr Taleb. From the perspective of portfolio insurance, that does not really matter. What matters it that its viral shock was enough to justify using some means of recouping losses from a blitzed portfolio. 

With household insurance, you pay the annual premium year after year and make no claims on the underwriter. Just occasionally, however – and not actually for everyone – an event comes along that makes all those little payments worthwhile. Insuring an equity portfolio works on the same principle. Most years the cost of the insurance – we will explain that shortly – will simply be a charge against profits. Instead of the annual return being, say, 10 per cent, it will be 8 per cent. However, sooner or later – and, crucially, more often than the statistics of normal distribution would have us believe – along comes the shock that generates a payout sufficient to offset all those little annual costs and perhaps to put the portfolio ahead of the game. 

Sounds great. What could possibly go wrong? Chiefly that, on average, the cost of the insurance is actually too high. AQR Capital, a US firm that manages $180bn-worth of hedge funds, has over the years argued that using traded options is “an overpriced means of getting portfolio protection”. And the firm sees nothing in 2020’s market convulsions to change its opinion. 

We crunched a lot of data from the FTSE 100 index over the past 10 years to see which view worked better for UK equities. The result – which, of course, may not be typical of any 10-year period – favours Mr Taleb; at least, it would if dealing in traded options was as easy for private investors in the UK as it used to be. 

First, let’s clarify what is meant by ‘portfolio insurance’. Protecting an equity portfolio against losses can take several forms and does not have to involve traded options. Generically, however, all other tactics come under the heading of ‘hedging’. That is, they protect a portfolio against some – but not all – of its losses and, ahead of the event, the degree of protection they will offer is mostly guesswork (see the box, ‘Planting hedges’ below). 

That leaves traded options – specifically buying put options – as the only real way to remove downside risk from a portfolio. That is because – as with conventional insurance – an investor pays someone else to assume the risk that he is unwilling to accept. That makes the party on the other side of the transaction – the counterparty – very important. An insurance contract is only as good as the reliability of the counterparty. In practical terms for retail investors, that is not a problem. The market on which they trade – in the UK, ICE Futures Europe – assumes the risk. 

First, however, each investor must decide whether or not to buy portfolio insurance. This is a matter of being able – or unable – to live with the price swings that always accompany investing in equities. Table 1 helps by quantifying the volatility since 2010 of the total-return version of the FTSE 100 index (ie, including the effect of dividends received); volatility, basically, being variation from average movements. This confirms the bounciness of equity prices. Typically, the multiple of the index’s minimum volatility to its maximum during a calendar year is over three times. When things get scary, volatility usually surges. In 2015 – a lossmaking year – the multiple was 4.3 times and, so far this year, it is 6.6 times. 
 

 
True, volatility includes nice swings – when the market rises – as well as nasty ones, yet fearful investors need only worry about those that are nasty. In other words, they should focus on how much they could lose and ask, what is the likelihood of big losses? Table 2 tackles this. Using the Bank of England’s wonderfully useful database, 1,000 years of English economic data, the table shows the frequency of severe falls based on monthly returns in London-quoted shares since 1900.  For completeness, the table shows data for month-on-month falls as well as falls over the previous 12 months. In practical terms, it is the 12-month falls that are relevant since they reflect the conventional way in which portfolio performance is measured. An investor would ask: what is the maximum level of running losses that I could live with before I need insurance? The answer will be subjective. It will depend not just on appetite for risk but when a portfolio needs to be monetised. 

Living with some risk goes with the territory. An investor who feels unable to cope with year-on-year portfolio losses running at 10 per cent probably should not be exposed to equities in the first place. Such losses are often just around the corner. Out of 1,444 months of data observed, losses were running at that rate on 198 occasions. That is about one month in seven, although, obviously, those months tend to cluster together in bear markets. 

Year-on-year losses running at 20 per cent or even 30 per cent are much rarer. In the case of 30 per cent, they are probably too rare. Table 2 shows that, on average, they crop up once every five years, or seven or eight times over a lifetime’s investing. In practice, the clustering effect means their appearance is much less. For instance, of the 24 months of 30 per cent-plus losses, six ran consecutively from October 2008 to March 2009. 
 

 
A similar point applies to losses running at 20 per cent or more. They come through on average once every 18 months, which sounds scary, but 35 of those 76 observations were bunched into just three bear markets. There were 10 each in the 10 months September 2008 to July 2009 and the 11 months July 2002 to May 2003. Then – worst of all, when UK capitalism seemed close to collapse – the market’s year-on-year losses topped 20 per cent 15 months running from December 1973 to February 1975. 

Despite this clustering, informal data browsing indicates that investors should expect phases when they will be nursing 20 per cent-plus losses once or twice every 10 years and so six to eight times over a lifetime’s investment. Intuitively, that sounds frequent enough to warrant crisis insurance, especially for those whose investment horizon is approaching its end. But what of its cost? No surprise to learn that insurance against falling prices has been expensive this year. Table 3 overleaf shows what an investor would have paid recently. The most important column is the one on the extreme right showing the annualised cost of put options on the Footsie.
 

 
To explain, let’s take the contract running to June 2021. This gives the holder the right to sell the index at 4500. This is 25 per cent below its level of 5995 when the data was taken, which is more or less around the parameters we have set. An investor would have paid 162.5 for that privilege, which is 2.7 per cent of the index’s value. Since the option had just about a year to expiry, then2.7 per cent was also its annualised cost. 

Note, however, that the Footsie would need to fall more than 25 per cent before investors could be sure of making a profit since the cost of the option must also be accounted for. Work that in and that contract would not be in the money until the Footsie dropped through 4338.  There is also an important technical point to consider because these prices are for the FTSE 100 options most frequently traded on ICE Futures, so-called ‘European-style’ options. Such an option can only be exercised on its expiry date – always the third Friday in the delivery month – when, in the case of a put option the holder ‘sells’ his options to the underwriter. That said, there is every likelihood that they could also be sold profitably in the market. ‘American-style’ options, which can be exercised at any time before expiry, are available for the FTSE 100, but they are costlier than the European version since an underwriter is more exposed to being ‘put’ upon. 

Yet the big question remains: would a sensible investor want to pay the costs of insurance shown in Table 3? On the face of it, those premium rates look like punishing amounts to deduct from the returns of a typical equity portfolio, which might average around 8 per cent a year including dividends. 

The good news is that today’s cost of insurance is not typical and Tables 4 and 5 show a range of the effect of the cost of puts on equity returns, using the FTSE 100’s total return from 2010 to 2019 as a proxy. The implied cost of insurance comes from using Black-Scholes to estimate the price of put options depending on the Footsie’s volatility at the time of purchase. To reiterate, the lower the level of volatility, the lower the cost of insurance (ie, ‘put’ prices) and the smaller the drag on portfolio returns. 
 

 
The difference between buying insurance at its cheapest (best) and costliest (worst) is considerable. In Table 4, the key row is the bottom one, showing the average performance (ie, the arithmetical mean) over the 10 years 2010-19. Consistently buy insurance at the best rates on offer – in other words, using the lowest level of volatility within the relevant period – and portfolio performance is barely touched – a 7.8 per cent average return is trimmed to 7.5 per cent. Buy it consistently at the worst rates and the average return is almost halved to 4.0 per cent. Even buying insurance at average prices – which, one assumes, would be the most likely outcome over a 10-year period – gives a portfolio a fair knocking. The difference between average returns of 7.8 per cent with no insurance costs and 6.4 per cent, on average, might not sound too much, but it is a reduction of approaching a fifth. 

Table 5 takes this a stage further by showing in money terms the cumulative effect of buying puts at good, bad and average prices over the decade. Start with £1,000 on 1 January 2010 and that would have grown to £2,040 if it perfectly tracked the FTSE 100’s total returns without any costs. Always buying puts at the best prices available and £1,000 would have grown to £1,984; at the worst prices, it would have been £1,416 and at average prices, £1,781. In other words, being fortunate enough always to buy insurance at the best prices delivered 40 per cent more return than being unlucky enough always to buy at the worst. The table’s bottom row shows the compound annual growth rates delivered according to the cost of insurance. To buy insurance always at best rates means that its cost is barely noticeable – a 7.4 per cent growth rate without insurance is trimmed to 7.1 per cent. But at worst prices, the growth rate is more than halved – 7.4 per cent a year becomes 3.5 per cent. Surely no investor would want to take that scale of up-front hit.
 

 
However, remember what Nassim Taleb said – most years the premiums paid on put options are a charge against portfolio returns, a cost of doing business and it is the year that a black swan hoves into view – or a correspondingly dire event – that makes all those little payments worthwhile. In the period since the start of 2010, that notion has been a fair reflection of reality, as Table 6 shows. 

The data in the table assume that two-year put options are bought at the start of every calendar year and that those options come with the right to sell at 20 per cent below the FTSE 100’s opening level at the start of each two-year period. Put another way, holders would be in the money, or thereabouts, when the Footsie fell something over 20 per cent from its opening level. That would enable them to sell their contract and recoup some or all of their losses, depending on the extent to which the underlying value of their options contracts matched the value of their portfolio. 

In the first 10 years under review, there were no trading days when the Footsie closed 20 per cent or more below the opening level for each contract. Investors were only able to make profits from their puts (and so recoup some losses) in 2020 as the markets collapsed in March. So the put bought at the start of 2019, with the FTSE 100’s opening level at 6728, was in the money for eight trading days. And, more significantly, the one bought at the start of 2020, with the Footsie at 7604, was in the money for 49 happy days – and often substantially so. 
 

 
Table 7 brings it all together. The values shown in it are in terms of FTSE 100 index points. So it assumes that the opening value of a portfolio at the start of 2010 was the same as the Footsie’s 5413. Assuming the portfolio tracked the Footsie perfectly, then it would be worth 6235 at a recent level for the index. This ignores the effect of dividends received over the years, which is substantial but not relevant for calculating the utility of the put strategy. 
 

 
Onto the Footsie’s recent value would be added a dealing profit of 1040 Footsie points. This is derived from selling for 6034 the two-year put bought at the start of 2020 when the index bottomed out at 4994 on 23 March (in practical terms, a put would not have been written for that particular strike price – 6000 or 6050 would have been the most likely level). 

Netted off against the recent Footsie value and the dealing profits would be the cumulative amount of premiums paid over the years. In practical terms, there would be six lots of premium payments for alternate years starting in 2010. Their cost would depend hugely on the price of options in the market. Buy at the worst rates – determined here by what the Black-Scholes model tells us – and insurance costs would overwhelm market returns and dealing profits. As Table 7 indicates, £1,000 invested at the start of 2010 would have become £1,152 simply by tracking the index, but would be reduced to £854 if puts were consistently bought at their most expensive. Buy insurance at average premium rates and the net value would be £1,149, making the effect of the costs negligible. Buy at anything better than average rates and the strategy would be a success. 

Sure, the results shown here may not be typical of other 10-year periods or of what to expect over a life-time’s investing. Nevertheless, an enough data was crunched to make the findings interesting. 

Also, in the real world costs have to be added in. In particular, there is capital gains tax (CGT). Options are, more or less, treated the same as ordinary shares for the purposes of CGT. Losses are tax deductible (and that includes the losses on options that expire worthless) and profits are taxed in the normal way. That is significant for investors who keep their equity portfolio within an Isa wrapper, since options are not eligible investments; however – slightly confusingly – they are eligible for inclusion within a Sipp. That makes for messy solutions. 

It is a further hindrance that so few private-client stock brokers and investment platforms offer traded options dealing in their services. Not just that but, among full-service brokers who claim to do so, the level of expertise may be lacking. At least two such that we spoke to – who, for now, should remain nameless – were unable even to provide details of their dealing charges let alone answer some simple technical questions. 
Perhaps this is proof that private-investor dealing in traded options has become a minority sport. Pity because it’s a sport worth pursuing.

Planting hedges
Hedging is the alternative to using traded options to protect a portfolio’s value. Various hedging tools are cheaper and more tax efficient than options, but they are not so effective. Gold and fixed-interest bonds are most often cited in this context and exposure to both of these is available via London-listed exchange traded funds (ETF), which are eligible for individual savings accounts (Isas) and for self-invested personal pensions (Sipps). 

True, gold often does a fair job at hedging equities. It is not just that its price surged in the early months of 2020 as equities tanked. More important, over the 10 years 2010-20, the covariance between the FTSE 100 and the dollar gold price has been minimal, meaning that, on average, the price of each moved independently of the other. That should be useful for hedging. 

Fixed-interest government bonds used to be the archetypal hedging tool. After all, interest rates would fall when the macroeconomic factors that depressed share prices were at their most formidable; and falling rates would make fixed-coupon bonds more valuable. But that was in the days when the developed world ran on interest rates that were high enough to go lower. For the foreseeable future, those days have gone. Sure, government bonds can still be a safe haven when fear and uncertainty are rampant, but that is not quite the same as saying they are sensible hedging tools – and certainly not when bonds are lumped together into bond funds. 

Other so-called hedging tools are more likely to be a great way for equity investors to lose money. Take ETFs that are so-called ‘reverse trackers’. If the tracked index falls 1 per cent on a trading day, the reverse-tracker fund will rise 1 per cent. Superficially, that might seem like a good way to hedge a portfolio, especially as these ETFs are also eligible for Isas and Sipps. However, the daily compounding by which reverse trackers work means that over the long haul – and assuming that equity markets move more up than down – they are certain to lose money. For example, divide £2,000 equally between the FTSE 100 and Xtrackers FTSE 100 Short (XUKS) in October 2012 (the earliest date for which we have data) to the present. By early June that £2,000 would have been turned into £1,657, with all of the losses coming from XUKS – its £1,000 would have become £560. 

Much the same can be said of contracts for difference (CFDs) and spread betting. Not for nothing do websites for trading in these products warn that 75 per cent of retail customers lose money. That is because both spread betting and CFDs, which should be useful tools for offsetting risk, are tailored to make long-term hedging prohibitively expensive. That just leaves short-term punting. Sure, these products, which run on the same principles, are fun for the occasional flutter, much like betting on the horses. But, as a serious tool for serious investors, they don’t figure.

Black-Scholes: a primer
Ask Warren Buffett about the Black-Scholes options pricing model and he’ll chuckle into his cherry Coca-Cola. One half of the brains behind Berkshire Hathaway (US:BRK.B) will say that he and his business partner, Charlie Munger, just love to exploit the pricing anomalies that the model throws out. In a way, that’s the trouble with the Black-Scholes model, it is too successful and so it shapes options’ prices even when it shouldn’t. 

True, the model has its shortcomings. But its success is based on its wonderful elegance. It compresses into a straightforward bit of maths the facts and intuition that go into generating plausible values for a financial option, a so-called ‘derivative’ that gives its holder the right – but not the obligation – to buy or sell a specific asset at a specific price and within a specific time frame. In its formula, there is all the information needed to value an option and nothing that’s superfluous. 

Just seven inputs are needed to work Black-Scholes and six of those are known in advance; only the seventh causes problems. 

Let’s work through these with reference to Table 8. First, there is the price of the underlying security on the day the option is written. In our example, that’s 6327 for the FTSE 100. Second is the exercise price. Almost exclusively we are dealing with insuring a portfolio against a market fall, so we will focus on puts, even though intuitively they are more difficult to grasp than calls. So let’s set the exercise price at 5000, about 20 per cent below the Footsie. 
Click here to go to an Excel spreadsheet of Black-Scholes that can be used to value both options to buy (‘calls’) as well as to sell (‘puts’).

Third, is the date of the deal and fourth is the option’s expiry date – in this case, June 2022 since we are dealing with long-term insurance against big losses. The fifth and sixth inputs deal with the time value of money, either received or foregone. The payments in question are the interest payable from money on deposit and any dividends received from the underlying security; in our example, that is the average yield from the FTSE 100. The values used in the table are 0.5 per cent for money on deposit and 3.5 per cent for the dividend yield. 

Other things being equal, for holders of a putoption, value rises in line with a rising dividend yield because, implicitly, holders already own the security that they have the option to sell and therefore receive the dividends. Simultaneously, put option value falls as interest rates rise because capital cannot be put on deposit if it is tied up in the security in question. For holders of call options, the opposite applies. 

That leaves the seventh input – a measure of the volatility in the underlying security’s price. Arguably, this is the crucial one both because it has the biggest influence on an option’s value and because it is the only input that has to be estimated. 

It is logical that volatility will influence options’ values in a big way – the more the market price of a security bounces around, the more that underwriters face the risk they will be obliged to buy the security at below its market price. Therefore, they will demand compensation for that risk in the shape of a higher premium. Insurance will become more expensive. 

But how volatile will stock prices be? There is almost no way of telling, so Black-Scholes takes the past as its best guess. It uses the annualised standard deviation of previous daily percentage changes in prices and it assumes that future price changes will be normally distributed around their average (ie, that there will be no feedback between past, present and future changes). This is a big shortcoming. Yet even normal distribution can produce wildly different figures for volatility – should the input into the model be current volatility, its average over a longer period, or its maximum or minimum values within a range? 

That will be a subjective decision driven by how confident or fearful options underwriters feel. The table uses the average volatility of the past 30 trading days. At 35.6 per cent, that’s high and appreciably higher than the volatility implied by actual market values of similar Footsie puts at the time of writing. Besides, go back to January and the figure would have been less than half that, in the process cutting the cost of an otherwise-identical put option by three quarters. 

Yet this exercise also highlights what is, arguably, the model’s most important use – not to value options but to get a fix on a financial market’s sentiment. Tweak Black-Scholes, inputting the known variables including options prices, and the output becomes implied future volatility or – as it has become known – the market’s fear index.