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Suppose an asset management company is in charge of strategic analysis. It is a situation in which the expected performance of the strategy should be analyzed through backtesting or simulation. Introduce in detail what techniques and processes you will use to conduct the expected performance analysis and explain why.
If I imagine myself as an investment strategy analyst working for an asset management company, I would do both backtest and simulation for measuring the performance of the strategy. The reason why I would do both is that backtest and simulation both have different strengths and weaknesses. For backtest, historical data is directly used, so past returns are reflected as they are and performance can be measured intuitively. However, there's no guarantee that the same historical data will be repeated in the future. For that matter, it is wise to conduct simulations using statistical information from historical data. Unlike the backtest, which can only analyze one scenario based on historical data, simulation has the advantage of measuring future performance because it can think of more cases through countless possible scenarios. However, since backtest are widely used in measuring performance in the actual market, it is better to include backtests, not the simulation alone. Both ways would have proceeded.
[Introduction of model]
To explain how I will measure the expected performance of the strategy, let's assume the model first. The model is what I created.
The model is a regime-based optimized portfolio model. From NBER, the economy regimes can be defined and a regime prediction model is also added for catching regime-switching signals. Once the regimes, such as expansion and contraction, the historical returns of the portfolio in each period can be rearranged into their own regimes. Once the rearrangement occurs, the best optimization model with certain constraints can be chosen. For the simulation, the distributions of each expansion period and contraction period's historical returns can be measured through multivariate normal distribution. By the Markov chain model, the probability of regime switching can be measured for the task of simulation.
In the case of backtesting, whenever the regime prediction model catches the regime-switching signal, the optimization model can be changed for asset allocation. Like the picture above, through the overall historical data that will be used for the backtesting, each regime period has a different optimization model. The blue-colored weight is from the expansion regime optimization model and the red one is from the contraction one. The lookback period is all available to backtest historical data from the moment of optimization. The reason why I chose the lookback period to be from the beginning of backtest historical data is that contraction and expansion returns are combined, and if the lookback period is too short, there can be a case that the optimization for the expansion period will be conducted only from contraction period data. So the available past backtests historical data from the moment of optimization will be the lookback period, so the data can be reflecting both of contraction and expansion period of data. I assumed that the transaction cost would not be considered here, so asset allocation and rebalancing occur frequently. Whenever rebalancing is conducted, the expected return will be measured. With all of the expected returns, the performance can be measured through different performance indicators, such as mean return, volatility, MDD, VaR, CVaR, etc. And the performance can be compared between contraction and expansion regimes or all together as well.
In the case of simulation, once each regime data's historical return distribution is measured the log return's mean value and standard deviation can be also measured. Additionally, the possibility of the occurrence of the current state and of other states can be defined from the Markov chain model. Let's assume that the beginning state is an expansion regime. From the uniform distribution, the values from 0 to 1 can be randomly chosen. The chosen values can randomly sample the error for GBM. If the sampling value is from 0 to 1-p, the next regime is following the expansion (current) regime, whereas, if it is from 1-p to 1, the next regime will be the contraction (other) regime.
In this way, one scenario of portfolio asset returns can be created, which can be repeated for simulation. When each scenario is created, the regime-switching can be also recorded. Through the regime records, a similar process of backtesting (optimization for asset allocation and rebalancing) can be conducted. Each scenario will have 'k’ number of portfolio returns that are combined with the optimized weights, where ‘k’ is the number of times. From this, each scenario's performance such as mean return, volatility, MDD, VaR, and CVaR can be computed. Additionally, by gathering the expected values of each scenario's returns, their performance can also be calculated.