The arguments in the following article have been made before and are well known among finance professionals and academics. Volatility as a convenient risk measure and -definition remains very popular, despite its many drawbacks. Given the importance of risk for investment decisions, this topic is worth discussing in more detail.


When discussing finance and investments, the term risk is almost always involved. There is talk about risk vs. return, value at risk, risk free rates and high-risk opportunities. Given the central role of risk in finance, it is remarkable how little thought is put into establishing what the term precisely means.

In non-academic finance, risk is mostly synonymous with volatility (the standard deviation of returns). However, is measuring the variability of returns really what investors care about?
The Merriam-Webster encyclopaedia dictionary defines risk as:

The possibility that something bad or unpleasant (such as an injury or a loss) will happen.

The important word is the word loss. Increased variability of returns is only a bad thing if the chance of losses increases. The classic example comparing 2 portfolios:

  1. A portfolio containing a risk free bond.
  2. A portfolio containing the same bond plus a call option on an underlying with uncertain future value.

At maturity, the first portfolio will be worth the par value of the bond. The second portfolio will be worth the par value of the bond plus the potential payoff of the option. Given the higher variability of possible outcomes, the second portfolio may end up having a higher volatility. It is doubtful whether it is also more risky from an investor's perspective, as in any case the value of portfolio #2 is greater than to equal to the value of portfolio #1.

Michael Keppler makes a similar argument in his well-known 1989 article Risk is Not The Same as Volatility (translated from the German article Risiko ist nicht gleich Volatilität).

Suppose the price of a stock goes up 10 percent in one month, 5 percent the next, and 15 percent in the third month. The standard deviation would be five with a return of 32.8 percent. Compare this to a stock that declines 15 percent three months in a row. The standard deviation would be zero with a loss of 38.6 percent. An investor holding the falling stock might find solace knowing that the loss was incurred completely “risk-free.”

These examples illustrate an important point: Volatility treats changes in returns to the upside the same as changes to the downside. If returns are distributed symmetrical around 0, this may make some sense. However, option payoffs clearly violate this assumption. As long as these returns are sufficiently skewed to the upside, a higher volatility is desirable for the investor.

Also, any backward looking measure faces issues when markets are in an extraordinarily quiet period. If there is indeed a new paradigm of low volatility and high returns, then everything is fine. On the other hand, if it turns out to be the calm before the storm (i.e. The New Economy or The Great Moderation), then basing investment decisions on historical volatilities may lead to suboptimal portfolios.

In fact, overheating markets, which are well in bubble territory often have such high returns combined with low volatility. This leads to further counter-intuitive results. A stock that has had spectacular low-volatility returns for the past 2 years will be seen as relatively risk-free. Even though it may be overvalued. If a crash happens and the stock price drops by 20% then the stock will have a higher (historical) volatility than before and hence more risk.


Risk Measures

Even non-contingent payoffs may be asymmetrical. Stock markets tend to crash once in a while, but they do not exhibit similar size upward spikes. On the other hand, some commodities such as wheat may experience the occasional upward spike. Also, at least according to the world view of value investors, undervalued stocks have returns skewed to the upside and a pure focus on volatility is misleading. In fact, even Harry Markowitz states in his Foundations of Portfolio Theory that:

Semi-variance seems more plausible than variance as a measure of risk, since it is concerned only with adverse deviations.

As a consequence, in academic finance volatility has long been considered a suboptimal risk measure.

After that, the question arises: What is a sensible definition of risk?

A number of other measures are common, here a short, non-exhaustive list of examples:

  1. Semi-variance (as mentioned above), or its square root semi-volatility. Instead of looking at all changes in the returns, only the negative ones are looked at. It was never very popular.
  2. Value at Risk (VaR) - Essentially a confidence interval, that determines the probability that the mark-to-market loss on a portfolio over a given time horizon exceeds a set value (i.e. a 5% probability that the loss on the portfolio will exceed USD1mm over 1 day). Note that there is no information on the expected size of the of the loss, should it exceed the threshold. It is very widely used, but also has many critics that consider its methodology flawed or at least insufficient. It is often used as a measure in risk management and risk controlling. Rick Bookstaber mentions in is blog post The Fat-Tailed Straw Man that Risk Managers are well aware of the limitations of VaR, and that the general critique on its use ignores the fact that it is typically just one number of many that risk managers are looking at:

    So, to recap, we all know that there are fat tails; it doesn’t do any good to state the mantra over and over again that securities do not follow a Normal distribution. Really, we all get it.

  3. Conditional Value at Risk (CVaR) - CVaR tries to overcome the shortcomings of VaR, by measuring the expected shortfall. It is sometimes used in conjunction with VaR and sometimes by itself, typically in portfolio management problems.

The obvious common feature of the three examples is the asymmetric nature of measurement - only the bad outcomes are considered.

A more thorough analysis of VaR and CVaR is beyond the scope of this first post on risk and may be done at a later stage.

Permanent Loss of Capital

Benjamin Graham defined risk as permanent loss of capital. This definition is more in line with intuition and works well qualitatively. However, it is more difficult to do quantitative analysis this way. Most investors do not wait until an asset has gone to zero before they sell. Hence, modelling the realisation of losses has to take into account idiosyncratic thresholds, where loss-making positions are closed out. Depending on the time horizon, the liquidity and the conviction of an investor about a position this level may change over time, which further complicates any analysis.

Stress Tests

A different approach is taken by Stress Tests, which enjoy popularity with both banks and regulators. A series of adverse scenarios is contemplated, and the impact on the entity in question is measured.
From the Wikipedia Stress Test page:
  • What happens if equity markets crash by more than x% this year?
  • What happens if GDP falls by z% in a given year?
  • What happens if interest rates go up by at least y%?
  • What if half the instruments in the portfolio terminate their contracts in the fifth year?
  • What happens if oil prices rise by 200%?
Such Stress Tests could theoretically be done on single positions, though this is not common. The insight that Stress Tests provide is trivial on most individual underlyings (i.e. what happens to a stock if equity markets fall by 20% across the board). Banks sometimes stress test their different trading books in such a fashion and regulators stress test bank balance sheets. The latest stress test by the Fed can be found here.
The advantage of Stress Tests is that they are not necessarily dependent on any assumption of the underlying return distributions. That does not make setting the adverse scenarios easy, but it avoids any reliance on normal distributions or complex modelling of fat tails.


The focus on volatility as a risk measure is not the result of some sinister conspiracy of high finance. It exists mainly because of a certain inertia of both banks and clients. Banks that want to sell products and services to clients have to speak their language. Portfolio managers that do not manage their own money have to speak the language of their bosses, investors and shareholders. In a way, even abstract concepts like volatility have a networking effect. Regardless of its real world merits, volatility as a concept becomes more useful, the more people know and use it. So everyone is using it because everyone else is using it.

Depending on the application, different risk definitions may be appropriate. Investors must be thoughtful when choosing, by which measure they estimate the risk they are taking. Keeping Peter Drucker's famous quote in mind:

What gets measured, gets managed.

Looking at different risk measures and thorough analysis of the actual positions can help in understanding the likelihood of negative outcomes. In the end, having a good grasp of the risk of a portfolio is as much art as it is science.


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BitcoinsBitcoin Crash February 2014: NY Post author Jonathon M Trugman describes Bitcoin of being a 21st century Ponzi Scheme in this article. Despite all my reservations about the new crypto currency, I do not agree with this statement. First and foremost and Ponzi or Pyramid scheme involves a distinct element of fraud, there is no evidence of that to be seen anywhere. According to Trugman's definition, every non-income generating asset in a bull market can be a Ponzi scheme. A number of underlyings could fit such a definition when prices are going up:

  • Art
  • Wine
  • Antiques
  • Watches
  • Oldtimer Cars
  • Baseball cards
  • Non-dividend paying stocks etc.

The big difference is that the above items have a use besides being speculative objects. However, this does not tip the scale from bubble to Ponzi Scheme. Probably Mr Trugman wanted to add some drama by dropping the Ponzi word.

What we are seeing is more likely the repeated growing and bursting of bubbles. The article mentions Pump and Pump, which is possible, but hard to prove.  described Bitcoin as a speculative bubble back in December in his blog. The article shows how there are few transactions and a significant amount of hoarding. For now, it looks as if he was right about the bubble. Nevertheless, it would not be surprising if we continue to see very high volatility in the coming months. Also, the current level of around 600 (on 17Feb14) is still more than 3x higher than in late October 2013. If this is really a crash, then we may not have seen the end of it.

Bitcoin has had some very wild value swings before, in April 2013 the closing price fell from over USD214.86 on the 09Apr13 to below USD75.9 (source: Bitcoin Charts). On 10Apr13 it rebounded to 101.52, but nevertheless this is almost a 65% fall in value over a three day period.


On the graph above the latest turmoil looks even worse, but when looking at a logarithmic scale below, this is no longer the case (source of both graphs: Bitcoin Charts).


So Bitcoin has shown some resilience to shocks before. As long as people put a value on it, it will continue to be traded, even after the next shock. Unlike most Ponzi schemes, which have to balance a delicate system of cash flows and an untrue cover story, there is no such thing in the case of Bitcoin.

Despite all this, I have never been a big fan Bitcoin, in fact, I think it contains some flaws that a lot of the fans deliberately choose to ignore. This post will try to investigate them a bit further.

On the bitcoin.org website there is the following definition:

Bitcoin uses peer-to-peer technology to operate with no central authority or banks; managing transactions and the issuing of bitcoins is carried out collectively by the network. Bitcoin is open-source; its design is public, nobody owns or controls Bitcoin and everyone can take part. [...]

The message certainly looks appealing at first glance. It sounds empowering, it promotes open source and there is no central bank or government that will inflate away your hard earned savings. However, is this enough to create a viable currency?
Before digging deeper, it makes sense to define some desirable features of a functioning currency for its users:
  1. An efficient means to pay for goods and services.
  2. A reliable measure of the value of goods and services.
  3. A store of value.

Earning interest may be another, but secondary feature. Depending on the mandate of a central bank the store of value goal may be sacrificed for the greater good, but the other 2 points are well met by any G10 currency. In the current state of affairs Bitcoin barely passes #1, although that may change. Given it's massive price volatility it fails on #2 and #3. Some people have made a lot of money with Bitcoin, but their success depends a lot on market timing.

So if Bitcoin looks less like a standard currency, then what does it look like? In many ways, Bitcoin resembles gold and maybe silver. They also have set of properties that are part currency and part commodity. Understanding those may help understanding Bitcoin a bit better.

  • They are non-perishable
  • Their supply is finite and growing.
  • The value of gold is predominantly driven by investment flows. There is industrial use as well, but the effect on the price tends to be minor.
  • In physical form they are bearer instruments and can be traded without audit trail.
  • In physical form it is the owner's responsibility to protect against theft.
  • Leaving the industrial uses aside, gold does not have a lot of inherent value. It is mainly valuable because people consider it so.

Gold and silver obviously have a phenomenally long track record as means of payment, stores of value and safe havens. They are surely here to stay, however, at which price is not obvious. Bitcoin is still in much earlier stages and it remains to be seen how it copes. One potential weakness is, that the complete lack of alternative use could become a problem. If there is ever a crisis of trust, there is no fallback activity which keeps Bitcoin in circulation. In currencies, ideally, the powers and actions of the government and the central bank help to mitigate such crises.

To further analyse the viability of Bitcoin it is useful to distinguish two cases. It remains a niche currency that facilitates international payments and promotes privacy among other things. Alternatively it becomes a widely used substitute for the currencies we use now, a bit like using actual gold coins.

If it remains a niche product, the massive price volatility has to come down for it to be a useful means of payment. Also, the technology has to become user friendly and secure enough, so that people with average computer literacy can easily handle transactions and do not need to worry about theft of their savings. At least the user friendliness aspect will likely be solved at some point. As long as there is the perception of rampant use of Bitcoin for illegal drugs and arms trade there is also the threat of government intervention. If exchanges are targeted by legal action and the possession is deemed illegal, then this will threaten a meaningful niche existence, even if government cannot directly attack Bitcoin.  

If, on the other hand, it becomes a widely used currency, then additionally to the above points, a whole new set of issues arises. It would also have some issues of the gold standard.

Pawel Morski describes some of those issues in his blog:

I have nothing to say about the Gold Standard other than it’s the obvious solution for those who feel the main problems with the euro are that it’s too flexible and covers too few countries.

This highlights the problem of having a global currency in different countries with different growth rates of the economy and of credit.
By far the biggest issue in my view is the limited supply of Bitcoin. The protocol is designed such that there will never be more than 21 million Bitcoins. To be fair, according to this Investopedia article, this limit will only be reached in 2140. In a world where Bitcoin has been widely adopted, the 21 million limit is reached and the economy keeps growing at a positive rate, there is bound to be deflation. Because there is no way to do monetary policy, this may lead to unfavourable outcomes.
Inflation and especially Hyperinflation can create a strong emotional response in people. Even in an environment of mild inflation we remember how much cheaper things used to be. Also, the thought of losing most of one's savings in a short term through hyperinflation is deeply worrying. The point is though that deflation can have similarly dire consequences. In this WSJ interview, John Normand from the investment bank J.P.Morgan describes the trade off between inflation and deflation:

With fixed supply, bitcoin’s deflationary bias should also be clear. That quality serves owners well when exchanging into foreign currency, but it would be onerous for any economy operating with it as legal tender. Indeed Weimar Germany was unpleasant, but so was the Great Depression.

Bitcoin is a very interesting experiment, both social and also monetary, the Bitcoin Crash February 2014 does not change that. Bitcoin and other crypto currencies will likely provide a ton of study material for monetary theory and may well help getting to a better understanding of money and improve monetary policy by a great bit. However, I am not so sure whether it is the future of currencies some make it out to be.

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Third Party Calculation Agents

Third Party Calculation Agents have become more prevalent in the past years. Companies that run the strategy/index calculation as an outsourcing partner for the investment banks. This may not seem of great interest for the end client at first glance; however, there are some benefits to such an approach.

The calculation agent has very broad and discretionary powers. Banks that aim for a sustainable business will not abuse them, but there obviously is a conflict of interest. This excerpt is from the risk factors of an equity structured note.

If the calculation agent is the same entity as the guarantor and the issuer is an affiliate of the guarantor, potential conflicts of interest may exist between the calculation agent and the purchasers.

From a control point of view, it is an improvement to have an impartial third party involved calculating levels. It is true that the banks pay Third Party Calculation Agents, but this is a systematic process that can be verified, unlike CDO ratings for example.

The Third Party Calculation Agent can also provide some help/consulting on best practices for exception handling and some quality control for the rules to less experienced strategy providers.

In big and experienced investment banking operations, these advantages may not count for much, as they normally already follow best practices. Nevertheless, with the proliferation of smaller banks releasing Trading Strategy Indices, the potential for quality control as part of the work of Third Party Calculation Agents could grow.

For most clients, the existence of calculation agents other than the investment bank providing the investment strategy may not be significant enough to influence any investment decisions. Very sophisticated clients sometimes have to set up their own calculation spreadsheets, this could also be an area where Third Party Calculation Agents can leverage their knowledge and offer consulting services.

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trading strategy index exception handlingTrading Strategy Index Exception Handling is an important aspect of the Index rules.  They are purely systematic and do not contain discretionary elements. This allows investment banks and other brokers to offer these products to clients without having to acquire an asset management licence.
This sounds easy enough, however, coming up with rules that cover all possible cases and exceptions is more complex than meets the eye. Unlike rules for a trading strategy applied by a trader for a discretionary portfolio, it is not good enough to cover 80% of the cases and ‘wing it’ if necessary, once the rules no longer cover the situation. Even though this approach simplifies the rules creation process significantly and improves their readability, this can be interpreted as a discretionary element.


From a practical point of view, rules that do cover most cases and let the bank act in good faith in all other cases, could be a sensitive alternative. However, this is not how regulation works. Trading Strategy Index Exception Handling is a crucial aspect of best practices and regulatory compliance.

In an investment product that is sold to the public/qualified investors, this discretionary element can mean that a strict regulator (or compliance department) demands immediate action. Either doing an immediate update of the rulebooks or to stop dealing with such products. In the past, a number of banks were not very strict with their documentation, this is causing some headache now.If the nature of these exceptions is not clear, let me give some examples. Trading Strategy Indices and also standard index daily values are usually calculated using the closing price of the underlyings. In the case of a market disruption there may be no closing price, so there is the question how to deal with this.

  • Should a level for that day be published at all?
  • If yes, based on what?
  • Will they be previously published levels changed, once the disruption is over?
  • If the market is no longer disrupted, will there be some sort of backfilling of levels?
  • What if the disruption is for more than 1 day?
Extended market disruption is not common in equity and fixed income markets, but happens more often in the commodity sector. Rules that do in effect cover 100% of the cases need to answer the question of what happens on the fifth day of a market disruption or if a security is discontinued.

It is also worth mentioning that there is some reputational risk involved in dealing "in good faith". Even with the client's best interest at heart, the decisions made may still result in the client losing money. Unlike in the case of a purely algorithmic process, this can result in serious PR issues.

For providers of financial products it is crucial to have impeccable documentation of all offered products. Ambiguities and flaws in such documentation can give clients a free option to litigate in case the investment turns sour. This can cost costs banks a great deal of time, money, reputation and management capacity. Again Trading Strategy Index Exception Handling prevents all this.

In a world of ever more stringent financial regulation, there is little scope for less than complete complete rules on Trading Strategy Indices. Smaller and newer strategy providers may need some outside help on best practices, regulatory requirements and possibly on drafting the rules. This can come from law firms or other specialist providers in this field.
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Index Access WrappersIndex access wrappers are an important consideration in the investment process. Once client want to go for a specific Trading Strategy Index (TSI), they have to decide in which form to access them. Traditionally a lot of institutional clients went for over the counter (OTC) Excess Return Swaps or Total Return Swaps (on excess return and total return underlyings respectively). These are very flexible, but have become a bit less popular because of the involved credit risk and in some cases regulations like Dodd Frank require reporting to the authorities.

Some clients are also worried about credit risk and may not be ready for the operational burden of running a credit support annex (CSA) with reasonably high frequency.

When deciding on a certain index access wrapper or vehicle, clients have to consider the following aspects:
  • Flexibility
  • Speed of set up
  • (Marginal) Cost of wrapper
  • Complexity of set up
  • Regulatory limitations
  • Necessary documentation
  • Counterparty faced and quality thereof
  • Credit risk exposure to that counterparty
  • Mitigating factors on credit risk, such as CSA
  • Balance sheet costs (on the bank's side) which may affect pricing
  • Liquidity and potential penalty charges for early unwind


Possible alternative index access wrappers are medium term notes (MTNs) or certificates, issued either by the investment bank or a third party issuer. They can typically accommodate any underlying that would otherwise be accessed through a swap; however these notes are not very handy in case the client wants to trade in an out of a certain underlying with ease and low transaction costs. Also, unlike doing swaps, MTNs and certificates require the client to put up cash upfront.
Some banks have set up a number of their TSIs as ETFs. This allows investors to access strategies at very low transaction costs, negligible credit risk and balance sheet costs and great flexibility. On the other hand, if an institutional investor wants to make a sizeable allocation in more obscure strategies, the market maker in the ETF may not offer the whole size at the current offer price. Also, the client has to put up the capital upfront.

TSI set up as mutual funds share some of the features of ETF. Again low transaction costs (in the institutional share class), negligible credit risk and balance sheet costs and great flexibility are positive aspects. Bigger trades may lead to an increased tracking error until the fund provider manages to ramp up or unwind his positions to the new levels.

Setting up index access wrappers for highly flexible solutions is a bit more complex. Often a note is set up (typically SPV issued) that has some resemblance to a managed account or a portfolio bond. This note can be collateralised with high quality securities and could even contain a CSA with the swaps provider. With such a set up the client can enter excess or total return swaps with the full flexibility of the OTC set up. None of the credit and potential regulatory issues arise. The obvious downside is the complexity and the set up costs of such a construct and the fact that it will typically only accommodate one swap provider/bank. So either the client has to get these flexible notes in place with a number of banks or face a limited choice and potentially reduced negotiation power in fee discussions.Also, unless a bank has created an easily replicable template for such a setup, this will involve lengthy negotiations and significant upfront costs. Banks will typically only go ahead with such a product if they expect significant repeated business and fees.
Naturally no one size fits all, so investor clients have to weigh their alternatives. One can always change the approach if the current one turns out to be suboptimal.
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