Abstract:
Investors use different approaches to select optimal portfolio. so, Optimal investment choices according to return can be interpreted in different models. The traditional approach to allocate portfolio selection called a mean - variance explains. Another approach is Markov chain. Markov chain is a random process without memory. This means that the conditional probability distribution of the next state depends only on the current state and not related to earlier events. This type of memory is called the Markov property. Based on proposed approach, the possibility of testing the assumption of independence of the intervals selected a portfolio of distribution of a relationship between these values there. The presence of this dependency, consider a model based on Markov chain makes it possible. In this paper, assuming that independent portfolios can be modeled by a Markov chain model to describe different portfolio selection, Value at risk (VaR) and Conditional Value at Risk (CVaR). In fact, the portfolio return is selected, the ranges are divided into n range, each interval of a discrete Markov chains, we consider the situation. Finally, the results of this study indicate that the optimal portfolio selection based on Markov models arehigh performance but complex.
Machine summary:
"Based on proposed approach, the possibility of testing the assumption of independence of the intervals selected a portfolio of distribution of a relationship between these values there.
In this paper, assuming that independent portfolios can be modeled by a Markov chain model to describe different portfolio selection, Value at risk (VaR) and Conditional Value at Risk (CVaR).
Then we compare portfolio selection strategies obtained either by modeling the return distributions with a Markov chain or by using a mean–variance analysis.
Accordingly, in this paper we assume that interval dependence of portfolios can be characterized by a Markov chain so that we can describe different portfolio selections, VaR and CVaR models.
In portfolio selection problems we assume daily step with the convention that the Markov chain is computed on returns valued with respect to investor’s temporal horizon T .
If we denote with τ the investor’s temporal horizon, with Wt+τ −Wt the profit/loss realized in the interval [t, t + τ] and with θ the level of confidence, then the VaR is the percentile at the (1−θ) of the profit/loss distribution in the interval [t, t + τ]: VaRq ,t +t (Wt +t -Wt ) = inf{q | Pr(Wt +t -W £ q ) > 1 -q } On the other hand the CVaR measures the expected value of profit/loss given that the VaR has not been exceeded: We can think to use the Markovian tree to compute the possible losses (VaR, CVaR) at a given future time T .
In the second part we p( i )z(i) present some alternative markovian VaR and1 - q i: z( i ) £VaR An ex-post analysis on 60 days portfolio return distributions shows that the markovian tree better approximates the heavy tails than the Riskmetrics Gaussian model (B&S)."