AAAS

 
 

 
 

 
 

 
 

Why QMS Advisors    :

 
 

QMS Advisors has considerable experience in evaluating alternative strategies and in allocating to those strategies in our clients' total portfolio context. In addition to providing investment advice, to performing qualitative and quantitative evaluations of alternative assets, QMS Advisors has extensive experience in developing cutting-edge proprietary models to optimally devise strategic and tactical allocations across alternative strategies.

• Our conflict-free revenue model ensures independence and objectivity
  
• QMS Advisors was an early advocate of hedge fund and private equity and strategies for institutional clients
  
• QMS Advisors has developed advanced asset allocation models to account for alternative strategies' non-Gaussian return distributions
  
• QMS Advisors cutting-edge proprietary risk management models, in-depth manager research, and dynamic proprietary risk identification and exposure quantification methodologies is central to help identify and isolate top quality investment managers that meet our clients' unique needs
  

 
 

QMS Advisors consults to the broad spectrum of Alternative Investments:

 
 

• Portable Alpha Strategies
  
• Private Market Strategies:
  
  • (Venture capital, buyout funds, mezzanine debt, private debt, distressed debt, secondaries.)
    
• Hedge Fund Strategies
  
  • (Direct Partnership Investing, and Hedge Fund of Funds encompassing: Relative Value strategies, Event-Driven strategies, Tactical Trading and Macro strategies, and Equity Long-Short strategies)
    
• Real Estate and Global Infrastructure
  
  • (Core, Value-Added, Opportunistic strategies, Infrastructure)
    
• Natural Resources and Commodities (Oil & Gas, Timber, Agriculture) 
  

  
 

 
 

Overview Kalman Filter Functions

MATLAB MEX Function Reference
Kalman Filter (kalcvf.dll)

The Kalman filter provides a tool for dealing with state space models to analyse economic and financial time series of not only correlated its past values but also contemporaneously correlated each other and each other's past values. You can develop a model of the univariate or multivariate time series and the relationships between the vector time series.

Syntax


logl = kalcvf(data, lead, a, F, b, H, var)
logl = kalcvf(data, lead, a, F, b, H, var, z0, vz0)
[logl, pred, vpred] = kalcvf(data, lead, a, F, b, H, var)
[logl, pred, vpred] = kalcvf(data, lead, a, F, b, H, var, z0, vz0)
[logl, pred, vpred, filt, vfilt] = kalcvf(data, lead, a, F, b, H, var)
[logl, pred, vpred, filt, vfilt] = kalcvf(data, lead, a, F, b, H, var, z0, vz0)

Description


KALCVF computes the one-step prediction and the filtered estimate , as well as their covariance matrices.
The function uses forward recursions, and you can also use it to obtain k-step estimates.

The inputs to the KALCVF function are as follows:

data
is a Ny×T matrix containing data ( y1, ... , yT)'.
lead
is the number of steps to forecast after the end of the data.
a
is an Nz×1 vector for a time-invariant input vector in the transition equation,
or an Nz×(T+lead) vector containing input vectors in the transition equation.
F
is an Nz×Nz matrix for a time-invariant transition matrix in the transition equation,
or an Nz×Nz×(T+lead) matrix containing transition matrices in the transition equation.
b
is an Ny×1 vector for a time-invariant input vector in the measurement equation,
or an Ny×(T+lead) vector containing input vectors in the measurement equation.
H
is an Ny×Nz matrix for a time-invariant measurement matrix in the measurement equation,
or an Ny×Nz×(T+lead) matrix containing measurement matrices in the measurement equation.
var
is an (Ny+Nz)×(Ny+Nz) matrix for a time-invariant variance matrix for
the error in the transition equation and the error in the measurement equation,
or an (Ny+Nz)×(Ny+Nz)×(T+lead) matrix containing variance matrices for
the error in the transition equation and the error in the measurement equation, that is, .
z0
is an optional Nz×1 initial state vector .
vz0
is an optional Nz×Nz covariance matrix of an initial state vector .
The function returns the following output:

logl
is a value of the average log likelihood function of the SSM when the observation noise is normally distributed:

where Ct is the mean square error matrix of the prediction error , such that .
pred
is an optional Nz×(T+lead) matrix containing one-step predicted state vectors .
vpred
is an optional Nz×Nz×(T+lead) matrix containing mean square errors of predicted state vectors .
filt
is an optional Nz×T matrix containing filtered state vectors .
vfilt
is an optional Nz×Nz×T matrix containing mean square errors of filtered state vectors .
Algorithm

The KALCVF function computes the conditional expectation of the state vector zt given the observations, assuming that the mean and the variance of the initial state vector are known. The filtered value is the conditional expectation of the state vector zt given the observations up to time t. For k-step forecasting where k>0, the conditional expectation at time t+k is computed given observations up to t. For notation, Vt and Rt are variances of and , respectively, and Gt is a covariance of and . A- stands for the generalized inverse of A. The filtered value and its covariance matrix are denoted and , respectively. For k>0, and stand for the k-step forecast of zt+k and its mean square error. The Kalman filtering algorithm for one-step prediction and filtering is given as follows:

And for k-step forecasting for k>1,

When you use the alternative transition equation

the forward recursion algorithm is written

And for k-step forecasting (k>1),

Remarks

The initial state vector and its covariance matrix of the time invariant Kalman filters are computed under the stationarity condition

where F and V are the time invariant transition matrix and the covariance matrix of transition equation noise, and vec( V) is an Nz2 ×1 column vector that is constructed by the stacking Nz columns of matrix V. Note that all eigenvalues of the matrix F are inside the unit circle when the SSM is stationary. When the preceding formula cannot be applied, the initial state vector estimate is set to a1 and its covariance matrix is given by 106I. Optionally, you can specify initial values.
See also

KALCVS performs fixed-interval smoothing

Getting Started with State Space Models

Kalman Filtering Example 1: Likelihood Function Evaluation

Kalman Filtering Example 2: Estimating an SSM Using the EM Algorithm

References

[1] Harvey, A.C., Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge University Press, 1991.

[2] Anderson, B.D.O., and J.B. Moore, Optimal Filtering, Englewood Cliffs, NJ: Prentice-Hall, 1979.

[3] Hamilton, J.D., Time Series Analysis, Princeton, 1994.

Heightened Volatility to Hinder U.S. Economy as Credit Market Problems Persist

Heightened Volatility to Hinder U.S. Economy as Credit Market Problems Persist

Amidst the explosive growth in structural innovations such as collateralized debt obligations in financial markets in recent years, volatility has reemerged as a major concern. We believe volatility will remain above its long-term average over the next year and potentially will have substantial adverse effect on the U.S. economy.

The Chicago Board Options Exchange Volatility Index (VIX) reached a four-year high in August amid the turmoil in subprime mortgage and commercial paper markets. Concerns with the state of the U.S. housing and corporate credit markets and structured investment vehicles have led to doubts about the global economic outlook. The housing sector remains weak with most forward-looking indicators of U.S. housing demand pointing to a further deterioration in sales in the short-term. High-yield corporate bond spreads have surged since June to near their highest levels in four years as the chaos from the subprime mortgage market spread. The days of companies having easy access to the credit markets no longer exist.

This rise in economic uncertainty has led to higher market volatility since the VIX reached a five-year low in January. In this paper, we employ quantitative techniques to explain the causes of the rise in systematic risks observed in the market. Investment risks can be divided into systematic and unsystematic risks. Systematic risks refer to non-diversifiable risk factors that are compensated by an expected risk premium. Unsystematic risks, which are investment specific, are idiosyncratic and can be minimized through diversification. While unsystematic risks are known to mainly reflect microeconomic shocks affecting assets’ relative prices, systematic risks are recognized to mainly reflect macroeconomic shocks. We employ a framework that decomposes observed levels of market volatility or systematic risk into key economic and financial variables. Systematic risks, the implicit market price of risk, merely become a function of the selected fundamental explanatory variables introduced in the model.


The Relationship between the Standard & Poor’s 500 Implied Volatility Index (VIX) and Significant Economic Variables.

We analyzed the relationship between a range of financial and economic variables and the S&P 500 implied volatility index. Theory and empirical evidence suggest that the weekly log-differences of the implied volatility index can be explained in the order of importance by the following variables: equities as shown by the S&P 500 Index, volatility, changes in the yield curve, movements in the volume of open interest, oil prices and the U.S. Dollar Index.

Based on our analysis, these variables consistently influence the implied volatility index with negative S&P 500 returns having the most impact.

We observed a positive relationship between the historical and implied volatility indices (clustering effect), and a negative relationship between the implied volatility index and the underlying stock returns. This second phenomenon is asymmetric in nature -- negative index returns have a greater impact on implied volatility as an increase in the equity of the firm decreases the companies’ debt-to-equity ratio (leverage effect) and therefore risks.

The effect of changes in the yield curve level and slope are unclear -- an increase in interest rates decreases both the value of debt and equity. The impact of increasing interest rates on firms’ debt-to-equity ratio and therefore on volatility is as a result ambiguous. In addition, the effects of higher short-term interest rates over the period were typically offset by a flattening or inversion of the yield curve.

We also observed that currency appreciation has led to decreases in systematic risks in that currency’s economy. While an increase in oil prices raises economy uncertainty and therefore is expected to increase systematic risks. Finally, the volume of contracts traded in the underlying index is expected to be positively correlated with systematic risks.

Based on our volatility model, all significant factors can be considered when inferring the evolution of future short-term volatility levels.
Significant swings in stock indices should sustain higher levels of systematic risks
Higher levels of historical volatility should cause comparatively increased levels of systematic risks (clustering effect)
The effect of lower short-term interest rates should in part be offset by a steeper slope of the yield curve
Continued depreciation of the U.S. dollar and higher crude oil and commodity prices should also contribute to higher systematic risks

In conclusion, a large portion of the variance of the VIX is caused by identifiable factors. The tightening in corporate credit and continued weakness in the housing market have created economic uncertainties. In addition, the combination of the U.S. dollar falling against the currencies of its trading partners and crude oil trading near record levels boosts our expectations for volatility to remain above its long-term average over the next year.