This paper provides an econometric analysis aiming at evidencing the dynamics showed by the S&P 500 market index during the period of 4 January 2001–28 April 2020, in which the subprime crisis has taken place and the COVID-19 crisis has begun. In particular, we fit a three-regime switching model that allows market parameters to behave differently during economic downturns, with the regimes representative of the tranquil, volatile, and turbulent states. We document that the tranquil regime is the most frequent for the whole period, while the dominant regime is the volatile one for the crisis of 2008 and the turbulent one for the first four months of 2020. We fit the same model to the returns of the Dow Jones Industrial Average index and find that during the same period of investigation, the most frequent regime has been the tranquil one, while the volatile and turbulent regimes share the same frequencies. Additionally, we use a multinomial logit model to describe the probabilities of volatile or turbulent regimes. We show that, in the case of the S&P 500 index, the returns from the Volatility Index (VIX) index are significant for both the volatile and the turbulent regimes, while the gold, WTI oil, and the dollar indices have some explanatory power only for the turbulent regime.
Sovereign states issue fixed and floating securities to fund their public debt. The value of such portfolios strongly depends on the fluctuations of the term structure of interest rates. This is a typical example of planning under uncertainty, where decisions have to be taken on the base of the key stochastic economic factors underneath the model.We propose a multistage stochastic programming model to select portfolios of bonds, where the aim of the decision maker is to minimize the cost of the decision process. At the same time, we bound the conditional Value-at-Risk, a measure of risk which accounts for the losses of the tail distribution. We build an efficient frontier to trade-off the optimal cost versus the conditional Value-at-Risk and analyze the results obtained.
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