Financial risk management revolves about two options - to share or to transfer risk with/to somebody else. The two approaches are legitimate but they are substantially different in terms of their ripple effects. There are three main types of ripple effects: moral hazard, compounding and systemic. The first – moral hazard – is common to both options, but the second – risk compounding – is specific to the transfer of risk. Two examples are enough to clarify the differences between sharing and transfering.
Imagine a group of friends where one comes up with the following proposition: I just met an actuary who told me that there is high probability that one of us will be dead before we reach 65. So, why don't we join in to begin paying a monthly conttribution to buy a pension to the family of whoever has the misfortune of dying earlier? This form of risk sharing is the basis of any life insurance policy and it makes sense to pay a small amount into a pool of money to get life insurance. Of course, by feeling safer the participants in the insurance pool may become more careless and in the end instead of one death the actuary will come back with an estimate of two of them dying before they are 65. This is the so-called moral hazard of people taking more risks when they feel safer.
Now imagine the same group discussing about buying a couple of stocks in the Dow Jones index and their fear that they may turn out losers. Then one of them comes up with the following suggestion: why don't we pool our money together and buy all the stocks in the index, this way even if a couple of them turns out a loser the loss will be shared by all and we still get a return close to the market return. Actually this form of risk sharing is the basis of index-tracking Exchange Traded Funds (known as ETFs); and it makes sense to pay a small fee to a professional fund manager and incur the costs intrinsic to the small deviation from the index (the so-called trailing cost) to achieve a return close to the index. Of course, the more people adhere to this form of investment the more the index becomes volatile because whenever a constituent stock loses the confidence of investors they will dump not just that stock but the entire basket of stocks in the index. This increased volatility means increased risk and it is also part of the so-called moral hazard.
Moral hazard is inherent to any form of risk sharing but its consequences can be priced in the insurance policy or the fund manager’s fee. However, the alternative based on risk transfer may compound rather than reduce the risk. We may illustrate this process through the following example.
ETFs are one the fastest growing financial products. While there were less than 100 ETF funds a few years ago, now there are more than 4000 ETFs - 1300 created in the last two years – attracting more than $1.6 trillion. Currently the ETF offering covers all asset classes enabling investors to take leveraged or unleveraged long and short positions. Most of the newly established ETFs are synthetic products that replicate the returns of an index without owning the underlying securities using instead swaps, futures and other derivative products.
To understand synthetic ETFs imagine that while discussing the traditional form of risk sharing through ETFs one of the friends comes up with the following synthetic ETF alternative: Instead of incurring trailing error costs, why don't we simply ask my bank to invest the money into an alternative portfolio, including up to 10% in derivatives, and swap its return for a return that matches the exact index return?
However, one of his friends felt skeptical about his proposition and asked: but then we would be transferring the bankruptcy risk in a predefined set of 30 different companies into a single bank and an unknown portfolio which must have a higher probability of going bust? Sorry, I do not believe it is wise to exchange the risk of a trailing cost of less than 1% for a 10% bet in your bank and unpredictable losses in the alternative portfolio. This transfer would simply compound the risk we are already taking on the index.
Guys don't worry! First, we will ask a smart fund manager to run the alternative portfolio. Second, we may hedge the two legs of the swap with a hedge fund capable of unloading the risk to a bunch of investors with deep pockets to support any losses. Third, our bank is too big to fail and would be bailed out by the government in case of trouble. So, trust me, there is no chance that the probability of my bank going bust will be near the 10% implicit in your fear about compounding the risk.
Another skeptical added: but what about the systemic risk? Since most fund managers fail to beat the market why would your bank enter into an agreement which is likely to underperform the market or lose money?
Man, as I told you, on top of a synthetic ETF we may make a lot of money creating and selling a number of layers of asset pools backed by the pool in the alternative portfolio.
Sorry, the skeptical replied: wasn’t that the rationale behind the securitization that led to the subprime crisis and the collapse of Lehman Brothers? I do not buy it, because you will end up using some of those extra profits to bribe regulators and rating agencies into increasing the swap size beyond the 10% limit and by filling the alternative portfolio with lower and lower quality assets. By shuffling around the risks the risk you will not be shared but transferred and compounded. Instead you will build a house of cards doomed to be destroyed in a systemic earthquake.
To sum up, with the synthetic ETFs, there is a real risk of transforming what was an excellent risk sharing device into toxic assets that create a serious threat to the financial system.
Showing posts with label financial investments. Show all posts
Showing posts with label financial investments. Show all posts
Friday, 11 November 2011
Tuesday, 2 August 2011
Proof that One Should Not Put All the Eggs in the Same Basket
It is common sense that a simple form of risk mitigation is through portfolio diversification. This principle has been popularized as “do not put all the eggs in the same basket!” That is, do not invest all your Euros in a single investment. However, a few discordant voices claim that one should put all the eggs in a just a couple of baskets, so that they can be properly monitored.
The view proclaiming the advantage of diversification is based on the use of a statistical measure of dispersion called variance. It has the unique property that the variance of (a+b) is smaller than the variance of (a) plus the variance of (b). Since modern portfolio theory adopted variance as a proxy to measure risk it follows that the more securities one adds to a portfolio the smaller its risk. In fact, in most markets a substantial degree of risk reduction can be achieved by holding between 25 and 50 assets. So, a simple rule of thumb (for an equally weighted portfolio) is that investors should invest no more than 2 or 4% of their capital on each exposure.
In practice this simple rule has three major drawbacks: a) it is difficult to adopt by small investors without enough funds to buy economically at least 25 different assets, and is also hard to follow by those with large amounts of money without incurring excessive exposures to a single entity; b) exposures to 25 or 50 investments are hard to monitor by a single person; and c) most importantly, the expected risk reduction is strongly dependent on the degree of correlation between the different assets and correlations are extremely difficult to forecast.
On logical grounds it is clearly questionable to prove a property by choosing to identify it with something that has the property we wish to prove. In addition, it has also three more theoretical limitations: a) price and total return volatilities are not necessarily correlated with other important sources of risk, namely bankruptcy and market delisting; b) for some investment strategies volatility is more useful as a measure of opportunity rather than risk; and c) it does not fully accounts for the reduced returns caused by its implicit bias towards cash-like exposures.
So it seems worthwhile to add an alternative proof that reinforces the case for the superiority of diversification. Marginalist theories tell us that we should invest up to the point where the expected marginal efficiency of capital equals the risk free rate of return. This may be so at the aggregate level. But, when assessing individual investment opportunities, it implies that investors should invest as much as possible on the exposure with the highest expected returned, followed by the second and so on until they invest all their funds. For most investors this rule would mean investing their entire capital in the single most promising investment opportunity.
Yet, with the schedules of the marginal efficiency of capital sloping downwards (the normal textbook case), investing up to the point where it meets the free risk rate of return is not an optimal solution. To verify this imagine the case of an investor considering opportunities A and B with linear schedules sloping downwards. The first Euro invested in opportunity A has an expected return of 30% while the last Euro invested earns the same as the risk free rate of return, which is 10%. The first Euro invested in the second best opportunity B earns only 20% while the last earns the risk free return. As a result the expected total return for A is 20% and for B it is only 15%. Naturally, ignoring risk or assuming identical levels of risk, investors would put all their money into opportunity A.
This would not be an optimal solution, since by switching the last Euro invested in opportunity A to B it would earn 20% instead of 15%. Likewise one may improve the total return by switching the penultimate Euro and so on until it is no longer worthwhile. This point will be reached when the integrals of the two marginal efficiency curves in the two defined ranges are equal. In the numerical example given above an investor would be able to invest up to two thirds of his capital in opportunity B and still achieve a total return of 20%. However, his optimal allocation would be to invest two thirds into A and one third in B to achieve an expected total return of 21.67%.
Note that our proof of the supremacy of diversification was given under conditions of certainty. Should we wish to add risk we may consider a worst case scenario where the investment opportunity with the highest return has also the highest risk. We may, for instance, assume that the expected return of the first Euro invested in A might be missed by ten percentage points while that of B may be missed by only 2 percentage points. With these revised marginal efficiency curves the return for A would be 15% and for B would be 14%. Under this scenario investors could allocate up to 89% of their capital to B and still achieve a total return of 15%. But now the optimal capital allocation to A would be only 56%, with an expected total return for both assets of 16.78%.
Our simple model may be extended to more than two assets and to incorporate the effects of leverage and still prove the case for diversification. Its theoretical value is that it proves the case for diversification with or without risk (uncertainty). Its main practical drawback is the reliance on the marginal efficiency of capital curves which are not as easy to estimate as the volatilities. Still we believe that it will be enough to convince the few remaining skeptics about the superiority of diversification.
The view proclaiming the advantage of diversification is based on the use of a statistical measure of dispersion called variance. It has the unique property that the variance of (a+b) is smaller than the variance of (a) plus the variance of (b). Since modern portfolio theory adopted variance as a proxy to measure risk it follows that the more securities one adds to a portfolio the smaller its risk. In fact, in most markets a substantial degree of risk reduction can be achieved by holding between 25 and 50 assets. So, a simple rule of thumb (for an equally weighted portfolio) is that investors should invest no more than 2 or 4% of their capital on each exposure.
In practice this simple rule has three major drawbacks: a) it is difficult to adopt by small investors without enough funds to buy economically at least 25 different assets, and is also hard to follow by those with large amounts of money without incurring excessive exposures to a single entity; b) exposures to 25 or 50 investments are hard to monitor by a single person; and c) most importantly, the expected risk reduction is strongly dependent on the degree of correlation between the different assets and correlations are extremely difficult to forecast.
On logical grounds it is clearly questionable to prove a property by choosing to identify it with something that has the property we wish to prove. In addition, it has also three more theoretical limitations: a) price and total return volatilities are not necessarily correlated with other important sources of risk, namely bankruptcy and market delisting; b) for some investment strategies volatility is more useful as a measure of opportunity rather than risk; and c) it does not fully accounts for the reduced returns caused by its implicit bias towards cash-like exposures.
So it seems worthwhile to add an alternative proof that reinforces the case for the superiority of diversification. Marginalist theories tell us that we should invest up to the point where the expected marginal efficiency of capital equals the risk free rate of return. This may be so at the aggregate level. But, when assessing individual investment opportunities, it implies that investors should invest as much as possible on the exposure with the highest expected returned, followed by the second and so on until they invest all their funds. For most investors this rule would mean investing their entire capital in the single most promising investment opportunity.
Yet, with the schedules of the marginal efficiency of capital sloping downwards (the normal textbook case), investing up to the point where it meets the free risk rate of return is not an optimal solution. To verify this imagine the case of an investor considering opportunities A and B with linear schedules sloping downwards. The first Euro invested in opportunity A has an expected return of 30% while the last Euro invested earns the same as the risk free rate of return, which is 10%. The first Euro invested in the second best opportunity B earns only 20% while the last earns the risk free return. As a result the expected total return for A is 20% and for B it is only 15%. Naturally, ignoring risk or assuming identical levels of risk, investors would put all their money into opportunity A.
This would not be an optimal solution, since by switching the last Euro invested in opportunity A to B it would earn 20% instead of 15%. Likewise one may improve the total return by switching the penultimate Euro and so on until it is no longer worthwhile. This point will be reached when the integrals of the two marginal efficiency curves in the two defined ranges are equal. In the numerical example given above an investor would be able to invest up to two thirds of his capital in opportunity B and still achieve a total return of 20%. However, his optimal allocation would be to invest two thirds into A and one third in B to achieve an expected total return of 21.67%.
Note that our proof of the supremacy of diversification was given under conditions of certainty. Should we wish to add risk we may consider a worst case scenario where the investment opportunity with the highest return has also the highest risk. We may, for instance, assume that the expected return of the first Euro invested in A might be missed by ten percentage points while that of B may be missed by only 2 percentage points. With these revised marginal efficiency curves the return for A would be 15% and for B would be 14%. Under this scenario investors could allocate up to 89% of their capital to B and still achieve a total return of 15%. But now the optimal capital allocation to A would be only 56%, with an expected total return for both assets of 16.78%.
Our simple model may be extended to more than two assets and to incorporate the effects of leverage and still prove the case for diversification. Its theoretical value is that it proves the case for diversification with or without risk (uncertainty). Its main practical drawback is the reliance on the marginal efficiency of capital curves which are not as easy to estimate as the volatilities. Still we believe that it will be enough to convince the few remaining skeptics about the superiority of diversification.
Monday, 25 July 2011
Leverage as Friend and Foe
As far as I am aware there are only four legal ways to become seriously rich in a short period of time: to inherit or marry into money, to hit a lottery or sales jackpot, to become the CEO of a large public company or investment fund in the USA or to leverage one’s way into wealth. Out of the four, only leverage is not fundamentally determined by destiny or luck.
Not surprisingly, this explains why, throughout history, leverage never ceased to fascinate people as a kind of “Aladdin's lamp” for immense wealth. In fact, the history of financial innovation is little more than a continual re-invention of some form of leverage. Leverage or gearing is the percentage of external financing and it is often measured as the ratio of capital to debt or as the ratio of total debt to total assets.
Indeed, credit is an essential element of market capitalism. It allows those with entrepreneurial spirit to invest beyond their own capital and gives those without such spirit the chance to share in the success of entrepreneurship. This means that passive investors must accept a lower return to make it worthwhile for entrepreneurs to take the added risk.
The case to make debt-financed investments applies equally to families and governments. So, in a closed economy this might create an impossible situation where everyone wants to be a net borrower, leaving the central bank as the only net lender by creating the money necessary to fulfill the demand for debt. In such a system those in charge of dispensing credit have an extraordinary power over the fate of the borrowers.
In practice market economies rarely reach this extreme situation for three main reasons. First, many people cannot or do not bother to search for investment opportunities with returns well above the risk free rate of return. In particular, families and governments are often in this situation. Second, many do not have the collateral required by lenders or do not fulfill the requirements to access non-recourse finance. Finally, leverage is a double-edged sword and not all can or know how to cope with the risks of debt-financing.
To understand that there is a thin line between fortune and misery in the use of leverage, imagine that one can invest up to four times the value of his capital to achieve an expected return of 25%. If he succeeds his return will be 100%. But what if instead of an appreciation of 25% there is a loss of 25%? He would be completely wiped out.
The fact that the likelihood of a 25% loss is very small is not enough comfort because it will happen one day. And, if one keeps reinvesting all his proceeds, he will lose all his previous gains. Any roulette player knows this, but people often tend to forget it. Especially when prices have been going always in the same direction, as happened recently in the real estate market (many people had never observed a fall in housing prices).
So is it true that leverage, like death, in the end will always finish by catching us on the wrong side of the bet? Not necessarily, provided that we do not re-leverage all our gains, do not exceed a prudent level of leverage and manage it correctly (for instance by not carrying leveraged positions over-night).
To be prudent one needs to answer the important question of whether there is an optimal level of leverage and what are its determinants. Unfortunately, neither in theory nor in practice can we find an answer to this question.
First, different assets have different levels of volatility (for instance in the last 10 years, intra-day, the Dollar never fell by more than 4.8% in the Euro/Dollar market while in the stock market the shares of Microsoft never fell by more than 12%). Second, in itself, leverage changes the optimal composition of investment portfolios. Thirdly, because the optimal level of leverage may be above what lenders consider safe and lenders are often prone to stampede behavior creating wild fluctuations in what they judge as safe or not.
But, most importantly, at the theoretical level we find ourselves in a difficult position. This is true, even after ignoring the wild fluctuations in banker’s lending limits while considering only the spreads (or mark-ups) they charge to compensate for risk. Theoretically the optimal level can be defined as the level of leverage that maximizes the difference between the returns achieved with debt finance and those obtained without any leverage. The problem lies in the fact that the two curves depicting the marginal efficiency of capital cannot be derived separately.
In the absence of estimates for the optimal level of leverage, prudence dictates that one should err on the down side by keeping a reasonable margin below the level of debt capacity acceptable to lenders. This can be easily defined in relation to margin requirements or the present value of future free cash-flows. With this proviso and knowledge of the nature of debt-financing, investors may be able to turn a potential foe into a friend.
Not surprisingly, this explains why, throughout history, leverage never ceased to fascinate people as a kind of “Aladdin's lamp” for immense wealth. In fact, the history of financial innovation is little more than a continual re-invention of some form of leverage. Leverage or gearing is the percentage of external financing and it is often measured as the ratio of capital to debt or as the ratio of total debt to total assets.
Indeed, credit is an essential element of market capitalism. It allows those with entrepreneurial spirit to invest beyond their own capital and gives those without such spirit the chance to share in the success of entrepreneurship. This means that passive investors must accept a lower return to make it worthwhile for entrepreneurs to take the added risk.
The case to make debt-financed investments applies equally to families and governments. So, in a closed economy this might create an impossible situation where everyone wants to be a net borrower, leaving the central bank as the only net lender by creating the money necessary to fulfill the demand for debt. In such a system those in charge of dispensing credit have an extraordinary power over the fate of the borrowers.
In practice market economies rarely reach this extreme situation for three main reasons. First, many people cannot or do not bother to search for investment opportunities with returns well above the risk free rate of return. In particular, families and governments are often in this situation. Second, many do not have the collateral required by lenders or do not fulfill the requirements to access non-recourse finance. Finally, leverage is a double-edged sword and not all can or know how to cope with the risks of debt-financing.
To understand that there is a thin line between fortune and misery in the use of leverage, imagine that one can invest up to four times the value of his capital to achieve an expected return of 25%. If he succeeds his return will be 100%. But what if instead of an appreciation of 25% there is a loss of 25%? He would be completely wiped out.
The fact that the likelihood of a 25% loss is very small is not enough comfort because it will happen one day. And, if one keeps reinvesting all his proceeds, he will lose all his previous gains. Any roulette player knows this, but people often tend to forget it. Especially when prices have been going always in the same direction, as happened recently in the real estate market (many people had never observed a fall in housing prices).
So is it true that leverage, like death, in the end will always finish by catching us on the wrong side of the bet? Not necessarily, provided that we do not re-leverage all our gains, do not exceed a prudent level of leverage and manage it correctly (for instance by not carrying leveraged positions over-night).
To be prudent one needs to answer the important question of whether there is an optimal level of leverage and what are its determinants. Unfortunately, neither in theory nor in practice can we find an answer to this question.
First, different assets have different levels of volatility (for instance in the last 10 years, intra-day, the Dollar never fell by more than 4.8% in the Euro/Dollar market while in the stock market the shares of Microsoft never fell by more than 12%). Second, in itself, leverage changes the optimal composition of investment portfolios. Thirdly, because the optimal level of leverage may be above what lenders consider safe and lenders are often prone to stampede behavior creating wild fluctuations in what they judge as safe or not.
But, most importantly, at the theoretical level we find ourselves in a difficult position. This is true, even after ignoring the wild fluctuations in banker’s lending limits while considering only the spreads (or mark-ups) they charge to compensate for risk. Theoretically the optimal level can be defined as the level of leverage that maximizes the difference between the returns achieved with debt finance and those obtained without any leverage. The problem lies in the fact that the two curves depicting the marginal efficiency of capital cannot be derived separately.
In the absence of estimates for the optimal level of leverage, prudence dictates that one should err on the down side by keeping a reasonable margin below the level of debt capacity acceptable to lenders. This can be easily defined in relation to margin requirements or the present value of future free cash-flows. With this proviso and knowledge of the nature of debt-financing, investors may be able to turn a potential foe into a friend.
Saturday, 23 July 2011
Financial Investment – Art, Science or Gambling?
In principle, everything we buy can be treated as an investment and therefore to a large extent investment is like breathing, something that everybody knows about. However when dealing in financial assets we should avoid the traditional statement that investment is the commitment of funds with the hope of gain, or a process of buying and selling securities with a view to get the greatest possible return, or, more plainly, the art of buying low and selling high.
This is so because the services provided by financial assets (money, securities, contracts or hybrids) include the protection and transfer of wealth, the facilitation of partial ownership and the provision of liquidity. That is the utility we derive from them depends primarily not on its material use but on rotating our exposure to them so that we may profit from distributions and changes in their market value (mostly in secondary markets).
Thus, we define financial investment as “a process of rotation between financial exposures which at the time of our choosing will allow us to attain the highest possible net liquidation value above that achievable without rotation and risk”. This means that at any given moment in time we may compare the valuation of our holdings in long, short and hedged positions in financial instruments with the valuation of such portfolio in a previous date.
The success of exposure rotation is the result of skill and luck. The skills required depend on the investment approach chosen (day-trading, event-trading or portfolio management) as well as on the strategies pursued. The net returns achieved may be amplified or reduced through taxation and leverage which also require specific skills.
Like in many activities the skills are both innate and nurtured through practice and education. Thus skills must necessarily be a combination of art, science and gambling. And, specific strategies and instruments require different combinations. For instance, investing in derivatives is closer to gambling while investment in fixed-income securities is more reliant on science.
In terms of science we could look at investment as an optimization problem defined as the maximization of total return over a given time horizon subject to a number of risk constraints. However, because of the uncertain nature of the investment outcomes, this mathematical formulation of investment is not feasible.
Alternatively we may look at investing as a form of gambling. To draw analogies with gambling we must distinguish games that combine luck and skill, like poker and football, from those that are purely games of chance like the roulette or the lottery. This distinction is fundamental because investment can clearly be considered as a game of the first kind, a game that mixes skills with luck but not a game based on pure luck or randomness.
Finally, we may define the investment activity as an art, an art not only in buying and selling but an art in forecasting prices and in undertaking calculated risks. What distinguishes science from art is not the degree of science and technique used in a particular activity but rather the creative and aesthetic nature of the activity. This is crucial to spot short-lived market imperfections and in this regard some view investment as a craft while others consider it to be the last liberal art.
Our preference goes to classify investment as a liberal art, defined as an activity based on worldly wisdom achieved by developing mental models enabling investors to extract knowledge acquired through multidisciplinary approaches (including the traditional disciplines of accounting, economics and finance, but also physics, biology, philosophy, psychology and literature). To a large extent, such an art form must be developed on an individual basis and as a self-satisfying activity.
Unfortunately not everyone can be an artist. However, the beauty of market capitalism is that not all investors need to pursue the art of investment. They may outsource it to honest professional investors.
This is so because the services provided by financial assets (money, securities, contracts or hybrids) include the protection and transfer of wealth, the facilitation of partial ownership and the provision of liquidity. That is the utility we derive from them depends primarily not on its material use but on rotating our exposure to them so that we may profit from distributions and changes in their market value (mostly in secondary markets).
Thus, we define financial investment as “a process of rotation between financial exposures which at the time of our choosing will allow us to attain the highest possible net liquidation value above that achievable without rotation and risk”. This means that at any given moment in time we may compare the valuation of our holdings in long, short and hedged positions in financial instruments with the valuation of such portfolio in a previous date.
The success of exposure rotation is the result of skill and luck. The skills required depend on the investment approach chosen (day-trading, event-trading or portfolio management) as well as on the strategies pursued. The net returns achieved may be amplified or reduced through taxation and leverage which also require specific skills.
Like in many activities the skills are both innate and nurtured through practice and education. Thus skills must necessarily be a combination of art, science and gambling. And, specific strategies and instruments require different combinations. For instance, investing in derivatives is closer to gambling while investment in fixed-income securities is more reliant on science.
In terms of science we could look at investment as an optimization problem defined as the maximization of total return over a given time horizon subject to a number of risk constraints. However, because of the uncertain nature of the investment outcomes, this mathematical formulation of investment is not feasible.
Alternatively we may look at investing as a form of gambling. To draw analogies with gambling we must distinguish games that combine luck and skill, like poker and football, from those that are purely games of chance like the roulette or the lottery. This distinction is fundamental because investment can clearly be considered as a game of the first kind, a game that mixes skills with luck but not a game based on pure luck or randomness.
Finally, we may define the investment activity as an art, an art not only in buying and selling but an art in forecasting prices and in undertaking calculated risks. What distinguishes science from art is not the degree of science and technique used in a particular activity but rather the creative and aesthetic nature of the activity. This is crucial to spot short-lived market imperfections and in this regard some view investment as a craft while others consider it to be the last liberal art.
Our preference goes to classify investment as a liberal art, defined as an activity based on worldly wisdom achieved by developing mental models enabling investors to extract knowledge acquired through multidisciplinary approaches (including the traditional disciplines of accounting, economics and finance, but also physics, biology, philosophy, psychology and literature). To a large extent, such an art form must be developed on an individual basis and as a self-satisfying activity.
Unfortunately not everyone can be an artist. However, the beauty of market capitalism is that not all investors need to pursue the art of investment. They may outsource it to honest professional investors.
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