Distance from A to B and from B to A
Zhen and I were trying to increase portfolio diversification by introducing an additional fund. When the staring fund is an S&P 500 index fund, the diversification can be increased by adding a REIT fund. The level of diversification (we call them the distance between the two funds) is more than 60%.
Our first thought was that we could get the same level of diversification by adding S&P 500 index fund to a portfolio with a REIT fund. We used the exactly same methodology to determine the distance again. The new distance we got was less than 40%.
We were confused by these two results. How can the distance between two funds be different when measuring from a different staring point?
We looked at the mathematical equations which contained biased estimates of parameters. So this is one source which can explain why the distance estimates were different. This is the easy part since the mathematical equations are not the financial insights.
We first thought about explaining the difference from our daily experience. For example, if we are going to hire two software engineers to form a team with four skill sets, the sequence of hiring can be different. Suppose there are two engineers are qualified to form this team. Engineer A has three skill sets while Engineer B has two skill sets. One of their skill sets is overlapping between them. The team qualification is exactly the same. However, the difference hiring consequence may have different financial consequence. If Engineer A is hired first, then Engineer B may be hired at a lower cost. If Engineer B is hired fist, then Engineer A may be hired at a higher cost.
Another real life experience is that the diving form home to a downtown neighborhood restaurant can be different from the restaurant to home, especially if there are many one-way streets along the way.
The sequence of fund selection may be very important for portfolio construction as well. If we start with a bad fund, we may ultimately find the optimal portfolio, but the process may be very long. If we start with a good fund, we may find a similarly optimal portfolio, the process may be shorter. The two paths can be different.
It is my current expectation, the selection process should start with lest volatility fund. First we start with a 100% cash position. We gradually increase the number of funds in the portfolio by selecting the fund with least volatility to the highest volatility when other parameters are similar.
Higher risk is associated with higher return. The fund selection process is also from the lowest return fund to the highest return fund. If we select funds according to these two rules, we actually select fund along the risk-return frontier. This way we are increasing the risk-level and the return-level for each of the individual funds.
Our first thought was that we could get the same level of diversification by adding S&P 500 index fund to a portfolio with a REIT fund. We used the exactly same methodology to determine the distance again. The new distance we got was less than 40%.
We were confused by these two results. How can the distance between two funds be different when measuring from a different staring point?
We looked at the mathematical equations which contained biased estimates of parameters. So this is one source which can explain why the distance estimates were different. This is the easy part since the mathematical equations are not the financial insights.
We first thought about explaining the difference from our daily experience. For example, if we are going to hire two software engineers to form a team with four skill sets, the sequence of hiring can be different. Suppose there are two engineers are qualified to form this team. Engineer A has three skill sets while Engineer B has two skill sets. One of their skill sets is overlapping between them. The team qualification is exactly the same. However, the difference hiring consequence may have different financial consequence. If Engineer A is hired first, then Engineer B may be hired at a lower cost. If Engineer B is hired fist, then Engineer A may be hired at a higher cost.
Another real life experience is that the diving form home to a downtown neighborhood restaurant can be different from the restaurant to home, especially if there are many one-way streets along the way.
The sequence of fund selection may be very important for portfolio construction as well. If we start with a bad fund, we may ultimately find the optimal portfolio, but the process may be very long. If we start with a good fund, we may find a similarly optimal portfolio, the process may be shorter. The two paths can be different.
It is my current expectation, the selection process should start with lest volatility fund. First we start with a 100% cash position. We gradually increase the number of funds in the portfolio by selecting the fund with least volatility to the highest volatility when other parameters are similar.
Higher risk is associated with higher return. The fund selection process is also from the lowest return fund to the highest return fund. If we select funds according to these two rules, we actually select fund along the risk-return frontier. This way we are increasing the risk-level and the return-level for each of the individual funds.
posted by Unknown at 1:18 PM
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