It is always good to go back to basics for understanding how to develop effective investment decisions. Regardless whether an approach is systematic and quantitative or just qualitative based on the analysis of an expert, a decision framework is critical. I like to use some classic decision theory to help with context for any investment decisions.
Let's look at the simple framework that is associated with Bayesian decision analysis. Any decision is based on a decision space. The decision space is the combination of the set of all decisions "d" and the set of all possible outcomes or states of nature "z". Each combination of a decision and a state or outcome will lead to a result, a loss or a gain. In decision theory, the loss function is the outcome from the combination of decision and state, L(d,z). Decisions have consequences.
Clearly, there is a large set of possible states and decisions. A grid of choices based on events leading to pay-off or results. A trader just wants to find the combination of decision and state that will minimize the loss function. You can think of this large grid of decisions and states which form a set of losses but that doe snot help with what will likely happen.
You want to pick one decision based on what will happen. Of course, life is not that easy because each state has a probability of occurring P(z). Hence, we have to account for the expect loss, E(L) = sum of all possible results [L(d,z)*p(z)]. Minimizing the loss function is the same as maximizing return. If you know the chance of any state and the decision you will choose, you can get an expected return. Now you have something that can be worked with to get an idea of effective decision. You have a forecast problem based on probabilities and a decision problem of what action you would take for a given state.
Clearly, there is a large set of possible states and decisions. A grid of choices based on events leading to pay-off or results. A trader just wants to find the combination of decision and state that will minimize the loss function. You can think of this large grid of decisions and states which form a set of losses but that doe snot help with what will likely happen.
You want to pick one decision based on what will happen. Of course, life is not that easy because each state has a probability of occurring P(z). Hence, we have to account for the expect loss, E(L) = sum of all possible results [L(d,z)*p(z)]. Minimizing the loss function is the same as maximizing return. If you know the chance of any state and the decision you will choose, you can get an expected return. Now you have something that can be worked with to get an idea of effective decision. You have a forecast problem based on probabilities and a decision problem of what action you would take for a given state.
So let's add some simple stories to this model. The size of a trade could be limited which will have an impact on the loss function for any state. This is part of the decision, sizing. If you just go long, you will have a set of pay-offs. If you have an option strategy, you will get a different set of pay-offs. If you have a stop loss your decision will be to get out of a trade so the loss for a decision and outcome will be fixed and limited.
So simply put, differences in managers will be a function of the set of decisions that could be made for any state or outcome. Hence, if you want to know how managers differ, you have to ask what would be the decision that will be taken given a certain state. Even if managers have all the same forecasting skill, their returns will differ based on the set of decisions they will take for a given state. This is an important distinction.
This decision choice is really an easy problem before you add in uncertainty. If you know the state, the decision is obvious. Now, we add in the probability of the state and it becomes harder but still relatively easy to model. If you think that there are different probabilities for what the stock market level will do, you can make a decision for what action to take and you can compute the expected return. Going long or short is an easy decision. Buying an option is more complex but we will know what the loss function will be for any state of the market. Along with differences in decisions, the focus has to be on the probabilities that are constructed by the decision maker with respect to the states of the world. This is the differences in forecasting skill.
Understanding investment managers is always a two part process, what is their forecasting skill and who do they make decisions.
So simply put, differences in managers will be a function of the set of decisions that could be made for any state or outcome. Hence, if you want to know how managers differ, you have to ask what would be the decision that will be taken given a certain state. Even if managers have all the same forecasting skill, their returns will differ based on the set of decisions they will take for a given state. This is an important distinction.
This decision choice is really an easy problem before you add in uncertainty. If you know the state, the decision is obvious. Now, we add in the probability of the state and it becomes harder but still relatively easy to model. If you think that there are different probabilities for what the stock market level will do, you can make a decision for what action to take and you can compute the expected return. Going long or short is an easy decision. Buying an option is more complex but we will know what the loss function will be for any state of the market. Along with differences in decisions, the focus has to be on the probabilities that are constructed by the decision maker with respect to the states of the world. This is the differences in forecasting skill.
Understanding investment managers is always a two part process, what is their forecasting skill and who do they make decisions.
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