*Tid:***14 november 2002 kl 1515-1600 **

*Plats :***Sammanträdesrummet 3424 (innanför pausrummet)**,
Institutionen för
matematik, KTH, Lindstedts väg 25, plan 4. Karta! **OBS!** Dag och plats!

*Föredragshållare:***
Pauline Edlund.
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**Titel:** **
Improved Estimation of the Covariance Matrix, a Real Estate Application. (Master thesis)
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**Sammanfattning:
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The practical use of Markowitz portfolio optimization theory is limited partly because of the difficulty of forecasting the required input parameters. The input parameters are the return and covariances for all assets included in the portfolio. These parameters have to be estimated and the quality of the estimates is crucial for the chances to really allocate on the efficient frontier. The return estimates are important for an investor seeking a portfolio with high risk and return, and the covariance estimates are important for investors that seek the minimum variance portfolio (lowest possible risk). The purpose of this thesis is to find an estimation method for the covariance matrix that increases the chances of allocating close to the minimum variance point. Which estimation method that is preferable is dependent on the available data. This thesis wants to find an estimation method for estimating the covariances between real-estate sectors, and the data are very limited. The limited data make the error in the estimates large when the historical sample method is used. Another factor inf luencing the quality of the estimate is the size of the covariance matrix, on which level the investor wants to allocate. As the dimension of the matrix increases so does the estimation error. The dimension of the matrix is also important for which estimation method to use.

In this thesis we evaluate a factor model and use this model for forecasting covariance matrices of different dimensions. The method is tested on real data and with simulations. The method is compared with other methods like different Bayesian methods, principal component analysis and the classical, historic sample method. We define a good estimation method as a method that gives a stable solution to the Markowitz optimization problem and solutions close to the minimum variance point.

Result and theory shows that the widely used historic sample method often is out-performed by the factor model. An investor could decrease the risk in the portfolio (come closer to the true minimum variance point) by using a factor model instead of the historic sample method. How many percent the portfolio variance could be reduced varies from different matrix dimensions. The larger dimension, the greater are the positive effects of the factor model. Simulation shows that the factor model does give a more stable solution to the optimization problem. Tests on real data indicated that the historic sample method is outperformed by many other estimation methods. The limited data only allowed one test, and the result from this test showed that the variance in an optimized portfolio can be reduced by approximately 1 - 5 % by using a factor model instead of the historic sample method.