Les idées reçues

Selon cet article de mediapart, la spéculation financière est responsable de la montée des prix des matières premières, au moins dans une certaine mesure.

L’article se fonde sur un certain nombre d’idées reçues sans jamais apporter d’argument tangible et se contente de stigmatiser les “spéculateurs”. Et pourtant l’argument clé dans cette discussion est là, écrit noir sur blanc: “seuls 2% des acheteurs de contrats à terme se font effectivment livrer de la marchandise”.

Un peu de recul

Autrement dit, toute cette spéculation est essentiellement un jeu à somme nulle puisque la plupart des positions prises par les spéculateurs sont debouclées avant l’expiration des contrats. Certains auront gagné de l’argent, d’autres en auront perdu. Mais in fine, ce qui détermine le prix, c’est le fait qu’un vrai acheteur de la matière première va se faire livrer son camion de blé ou son cargo de pétrole, et qu’il va payer un certain prix de marché. Et inversement le producteur va se faire payer un prix de marché pour livrer sa production.

A partir de ce constat, on comprend que le prix final de transaction est essentiellement determiné par l’offre et la demande de cette matière première (meme si les spéculateurs peuvent avoir un effet à court terme). Et si le prix de marché était vraiment déconnecté de la réelle valeur marchande de ces produits (trop élevé), les vendeurs (les producteurs) se mettraient à produire plus de cette matière première du fait des marges plus importantes, ce qui ferait naturellement baisser les prix.

Par aileurs, de nombreux rapports de recherches montrent que la dérégulation des marchés de matières premières n’a pas eu d’effet notable sur la volatilité des prix, ce qui contrecarre la thèse proposée par l’article. Par exemple, deux chercheurs de l’université de Munster [1] expliquent:

We thus conclude that the increasing financialization of raw material markets has not made them more volatile.

Finalement, il ne faut pas oublier qu’une part non négligeable des intervenants sur les marchés de matières premières fournissent un service d’intermédiaire essentiel, à la fois aux producteurs et aux acheteurs finaux de ces matières premières, qui peuvent protéger leurs prix d’achat et de vente grâce aux marchés à terme.

Les solutions

Il n’y a pas des milliers de facons d’éviter la montée des prix des matières premières agricoles:

• Réguler les prix – le prix n’est plus determiné par l’offre et la demande mais par un texte de loi. Par définition, les fluctuations sont controlées. Mais cela coûte en général très cher – cf. les politiques de regulation des prix du pètrole au Vénézuela ou en Iran par exemple (coût de 84 milliards de dollars en 2008 selon l’Iran Daily Mail).
• Favoriser artificiellement l’augmentation de l’offre, via des subventions ou une régulation de la production. C’est ce qui a été fait pour l’éthanol et le principal impact a été de deséquilibrer globalement les prix des autres matières premières agricoles et de contribuer à la diminution de l’offre sur d’autres grains destinés à l’alimentation.
• laisser le marché et la loi de l’offre et de la demande jouer leurs rôles: lorsqu’un produit devient cher parce que la demande augmente, les producteurs (l’offre) vont naturellement augmenter la quantité de culture de ce produit. C’est un chemin malheureusement rarement choisi par les politiques.

Reférences:
[1]: Bohl, Martin T. and Stephan, Patrick M., Does Futures Speculation Destabilize Spot Prices? New Evidence for Commodity Markets (January 4, 2012). Available at SSRN: http://ssrn.com/abstract=1979602

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VaR Attribution using the Component VaR Approach

Calculating the variance-covariance value at risk of a portfolio is great but being able to identify how much each component of the portfolio contributes to the total portfolio VaR is even better. The Component VaR is one way to achieve that analysis.

Calculation of Parametric Variance-Covariance Value at Risk

The VaR over d days at a confidence level c is calculated as
$VaR(c,d) = F(c,d)\sigma$
where
$F(c,d) = \mathcal{N}^{-1}(c,0,1)\sqrt{d}$ is a scaling factor
$\sigma$ is the daily volatility
Note: $\sigma$ can be scaled back from a weekly, monthly or annualised volatility by applying the following:
$\sigma_daily = \frac{\sigma_weekly}{\sqrt{5}} = \frac{\sigma_monthly}{\sqrt{21}} = \frac{\sigma_yearly}{\sqrt{260}}$
$\sigma = \sqrt{\omega^t\Gamma\omega}$
where $\omega = \begin{bmatrix}\omega_i \end{bmatrix}$ are the weights of the securities in the portfolio,
and $\Gamma = \begin{bmatrix} \gamma_{i,j} \end{bmatrix}$ is the covariance matrix.

Component VaR

Concept

The idea behind Component VaR (CVaR) is to find a way of calculating the contribution to the total VaR of a portfolio of any sub-portfolios, including individual positions. Asusming $(P_i)_{i=1,n}$ is a partition of the total portfolio, i.e. the union of all the sub-portfolios is exactly equal to the total portfolio, the CVaR has the following properties:

• $\sum^n_{i=1}{CVaR(P_i)} = VaR(P)$, the sum of the CVaRs is the total VaR
• $VaR(P\setminus P_i) \approx VaR(P) - CVaR(P_i)$, if a sub-portfolio is removed, the impact on total VaR is approximately its CVaR
• if a sub-portfolio is a hedge, its CVaR should be negative

Definition

VaRDelta is defined by [Garman] as $\Delta=\frac{1}{\sigma}\Gamma\omega$
VaRDelta has the following interesting property:
$^t\omega\Delta = \frac{^t\omega\Gamma\omega}{\sqrt{^t\omega\Gamma\omega}} = \sqrt{^t\omega\Gamma\omega} = \sigma$

The Component VaR of the security i is then defined as $CVaR_i(c,d) = {^t\omega}_{\delta_{i}}\Delta F(c,d)$,
where $\omega_{\delta_{i}} = \begin{bmatrix}\omega_k \delta_{ik} \end{bmatrix}$ and $\delta_{ik}$ is the kronecker symbol.

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Definitions

Simple Returns are defined as
$R^S_t = \frac{P_{t+1}}{P_t} - 1 = \frac{P_{t+1} - P_t}{P_t}$
Logarithmic Returns are defined as
$R^L_t = log (R^S_t + 1) = log (P_{t+1}) - log (P_t)$

Main Properties

Simple Returns

Simple returns are additive accross securities. If $(\omega_i)_{i=1 \ldots n}$ are the weights of different securities within a portfolio, with linear returns $(R^S_{t,i})_{i=1 \ldots n}$, the linear return of the overall portfolio is
$R^S_{t} = \sum_{i = 1}^n \omega_i R^S_{t,i}$

Logarithmic Returns

Logarithmic returns are additive over time. If the logarithmic returns of a security over time are $(R^L_{t+i})_{i=0 \ldots T}$, the logarithmic return over the whole $[t, t+T]$ period is:
$R^L_{t->t+T} = \sum_{i = 0}^T R^L_{t+i}$
If a security follows a Brownian motion, its logarithmic returns are normally distributed.

Difference

The Taylor series decomposition of log is as follows:
$log(1 + x) = \sum_{i=1}^\infty (-1)^{(n+1)}\frac{x^n}{n}, \qquad \forall x \in ]-1,1]$
So the error of the log-return vs. the simple return is in $o(|x|)$ for returns under 100%.
Typically, the error is less than 0.5% for returns below 10% in absolute value. However, it reaches several percentage points above 15% and more than 10% for returns above 50% or under -40%. The following 2 charts illustrates the extent of the error for small and large values.

Moments

The mean of the log return can be approximated as follows: $\overline{R^L} \approx \overline{R^S} - 0.5\sigma^2_S$
The 2nd, 3rd and 4th moment are also affected.

Conclusion

Whenever the terminal wealth is assessed or returns can be higher than a few percentage points, log returns can lead to significant estimation errors.

References

• Hudson, Robert, Comparing Security Returns is Harder than You Think: Problems with Logarithmic Returns (February 7, 2010). Available at SSRN: http://ssrn.com/abstract=1549328
• Meucci, Attilio, Quant Nugget 2: Linear vs. Compounded Returns – Common Pitfalls in Portfolio Management (May 1, 2010). GARP Risk Professional, pp. 49-51, April 2010 . Available at SSRN: http://ssrn.com/abstract=1586656
• Pini, Sergio, Approximations of Portfolio Returns: Are the Errors Really Small? (December 10, 2009). Available at SSRN: http://ssrn.com/abstract=1521442
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1 University of Michigan Survey of Consumer Confidence Sentiment

1.1 Definition

According to Bloomberg, the index is a survey of consumer attitudes concerning both the present situation as well as expectations regarding economic conditions conducted by the University of Michigan. For the preliminary release approximately three hundred consumers are surveyed while five hundred are interviewed for the final figure. The level of consumer sentiment is related to the strength of consumer spending.

1.2 Latest Announcement

The latest announcement on August 12th showed that the University of Michigan Confidence Index had dropped to 54.9 when the market was expecting 62.0. That sharp drop to a very low figure by historical standards has raised concerns over the economy. Bloomberg News analysed the situation in the following terms:
“Aug. 12 (Bloomberg) — Confidence among U.S. consumers plunged in August to the lowest level since May 1980, adding to concern that weak employment gains and volatility in the stock market will prompt households to retrench.”
What nobody is saying is whether that index is a good indicator of future stock market performance, which is the only thing that matters in the end.

1.3 Is the University of Michigan Confidence Index good at forecasting stock market performance?

Although there is no significant relationship between the University of Michigan Confidence Index and stock market returns over the next 6 months, the Index works as a good contrarian signal for longer period. Over the 3 years that follow very low levels of the University of Michigan Confidence Index, the stock market generally performs well, whereas when the Index reaches 100 or more the stock market performance over 3 years is on average flat to negative.

2 Historical Data

2.1 Data

Bloomberg has data about the University of Michigan Confidence Index since January 1978:

Interestingly, it seems that low readings on the University of Michigan Confidence Index have more often than not coincided with market bottoms. The latest example being the lows of Q1 2009.

2.2 Generalisation

2.2.1 Short Term impact

The main caveat of the previous chart is the limited number of occasions when the University of Michigan Confidence Index has been below 60 (8 months out of 398 since January 1978) and the significant dispersion of returns following these announcements. The chart gives a more granular view on the relationship and the main conclusion seems to be that there is no relation between the University of Michigan Confidence Index and the short term performance of the stock market.

2.2.2 Long Term Impact

Over a longer time horizon, extreme levels constitute a good contrarian signal: the market has almost always had a positive performance over 3 years when the University of Michigan Confidence Index has fallen below 72.

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