BLSH Model - Half-a-Loaf Case

The graph shown here are for the Half-a-Loaf case. The colored lines are the four simulated results for SPY, total assets, risky capital, and cash reserve values.

In this case, there were more cash than risky asset at the beginning (2:1 ratio). The are negative values for the risky asset (meaning short positions are required for this simulation case). It is very clear a simple short strategy might not work well in actual operations. In real operations, taking short positions in a bull market needs a lot of confidences. So we feel we might not be confident enough to do so in actual mangement of portfolios.

However, we can gain insights from this case. Some of the current understandings are the followings.

(1) The ratio between cash and risky asset is very critical when setting up the initial portfolio positions. When there is too much cash relative to risky asset, we can easily run into a situation when we do not have enough shares to sell when the market continues going up as shown in this half-a-loaf approach.

(2) The total assets curve is very statble over the entire simulation period. It is more or less close to a straight line. This means the volatility for this case is very low. We can carefully device a balanced portfolio with very little volatility for the most conservative investors based on this case with improved parameters to control shares investing in the risky asset.

(3) Based on the previous three simulation models, we become more confident that we can optimize model parameters to improve the overall model results. The appropriate ranges for the basic parameters should be within the range already used in the three models.

BLSH Model - the Duality Case

When we let cash and risky assets change at the similar ways, we can observe that the cash asset (blue line) and risky asset (red line) move up at the similar rates. We call this case as the duality case because the dual (the cash and the risky asset) are moving together.

As we compared the total assets curve (green line) with the SPY (brown line) curve, we can observe the difference between them. The difference is expanding during the bull market; the difference is shrinking during the bear market. The two curves almost converge together during the worst time in the market from mid-2002 to early 2003.

Now the question is whether the two curves will converge again in the future. If they will converge, are there still incentives to hold the risky asset alone? I can not be fully confident to predict such a convergence. But I do understand the following insights based on this result.

(1) Holding risky asset is taking risks. At the same time, holding cash along is taking another kind of risks. It might be the two extremes in the case of duality can compensate each other in the long run with the minimum oveall risk.

(2) Market timing will add tremendous values if one can really do it correctly. If one can sell the risky asset when the price is high and buy it back when the price is low, he is becoming the guru of investment vey soon.

(3) If one realizes that he can not do market timing well, the duality case might be a balanced way to invest for the long run. Once in while (might be as long as 10 years), you will catch up with the guys who invest only in risky assets.

BLSH Model - the Base Case

Actually this is the base case for our BLSH model. The previous post was the result of the buy/sell factor of 1.07. Our base case was defined with the buy/sell factor of 1.06. However, the little change in buy/sell factor has made some difference in the model result. Based on this, we can state that the buy/sell factor is a sensitive parameter in the model.

One very critical simulation result is that the cash reserve is negative during the worst time of the bear market. That means we need to use margin to finance new purhases of risky asset shares. In real operations, we might not be able to do this due to many factors such as manager's confidence in the overall bear market conditions.

BLSH Model - B Case with BSF 1.07

The base case result from our BLSH Model is very promising. The brown colored line is based on the SPY closing price. The green line is our model result. Apparently the green line is less volatile than the brown line. Which line do we like? The brown line or the green line?

This was actually an alternative to the base case. The result shown here had an alternative buy/sell factor (BSF) of 1.07. We had defined our base case with the BSF = 1.06.

The base case result is posted on the following blog.

Numerically Quantified Diversification II

Yesterday we reported our first real case study result using Vanguard 500 Index Fund as the base fund. That was based on the assumption that some of the growth-orientated investors like to have this fund as their anchor fund.

For some other investors, they may like to have growth and income at the same time. We assume that these investors may use Vanguard Wellesley Income Fund as the anchor fund. For these investors, their diversification needs are different. The results posted here today are for the estimated ranking based our modeling efforts.

The ranking of diversification benefits of the 50 funds based on the Vanguard Wellesley Income Fund are listed below. We list them from the least diversification fund to the highest diversification fund. The difference between the two rankings (today versus yesterday) is clear.

Life Strategy Income Fund
Life Strategy Conservative Growth Fund
Long-Term Investment-Grade Fund
Long-Term Bond Index Fund
Long-Term Treasury Fund
Wellington Fund
Intermediate-Term Bond Index Fund
Intermediate-Term Investment-Grade Fund
Total Bond Market Index Fund
STAR Fund
GNMA Fund
Intermediate-Term Treasury Fund
Short-Term Investment-Grade Fund
Short-Term Bond Index Fund
Balanced Index Fund
Life Strategy Moderate Growth
High-Yield Corporate Fund
Asset Allocation Fund
Equity Income Fund
Windsor II Fund
REIT Index Fund
Life Strategy Growth Fund
Selected Value Fund
Global Equity Fund
Health Care Fund
Dividend Growth Fund
Convertible Securities Fund
Windsor Fund
Value Index Fund
International Value Fund
Strategic Equity Fund
Small-Cap Index Fund
Total Stock Market Index Fund
European Stock Index Fund
International Growth Fund
Growth and Income Fund
500 Index Fund
Total International Stock Index Fund
Extended Market Index Fund
Morgan Growth Fund
Explorer Fund
Energy Fund
Growth Index Fund
PRIMECAP Fund
US Growth Fund
Precious Metals and Mining Fund
Emerging Markets Stock Index Fund
Growth Equity Fund
Capital Opportunity Fund
International Explorer Fund

Numerically Quantified Diversification I

We are reporting our first real case study result today. Diversification is very critical in portfolio management. However, there are no quantitative values for the diversification benefits. We are the first to quantify the diversification based on numerical values.

We used Vanguard family of funds as our first real case study. We selected 52 funds with data records over the last 10 years for this case study. We thought that the Vanguard 500 Index Fund as the base fund. The ranking of diversification benefits of the 50 funds based on the Vanguard 500 Index fund are listed below. We list them from the least diversification fund to the highest diversification fund.

Growth and Income Fund
Total Stock Market Index Fund
Growth Index Fund
Morgan Growth Fund
Value Index Fund
Life Strategy Growth Fund
Asset Allocation Fund
Equity Income Fund
Balanced Index Fund
PRIMECAP Fund
Life Strategy Moderate Growth
US Growth Fund
Windsor Fund
Windsor II Fund
STAR Fund
Strategic Equity Fund
Extended Market Index Fund
Wellington Fund
Dividend Growth Fund
Life Strategy Conservative Growth Fund
Growth Equity Fund
Small-Cap Index Fund
Health Care Fund
Global Equity Fund
Explorer Fund
Life Strategy Income Fund
Convertible Securities Fund
Wellesley Income Fund
European Stock Index Fund
International Growth Fund
Selected Value Fund
International Value Fund
Total International Stock Index Fund
Capital Opportunity Fund
Short-Term Investment-Grade Fund
High-Yield Corporate Fund
GNMA Fund
Short-Term Bond Index Fund
Energy Fund
Total Bond Market Index Fund
Intermediate-Term Investment-Grade Fund
Intermediate-Term Treasury Fund
Intermediate-Term Bond Index Fund
REIT Index Fund
Long-Term Investment-Grade Fund
Long-Term Bond Index Fund
Long-Term Treasury Fund
Emerging Markets Stock Index Fund
International Explorer Fund
Precious Metals and Mining Fund

Distance between Two Funds

In our first project, we studied all major traditional asset classes, such as the style box funds, the sector funds, bond funds, and REIT funds. We have defined a new concept in asset management – Distance. The distance concept is a quantitative representation of diversification. Before us, the diversification is just a qualitative concept. Now we can give a number for the level of diversification when two funds are considered in a portfolio. At a later stage, we will try to determine the multi-dimensional distance concepts for a portfolio with more than two funds.

When the large cap fund is the center, the five funds with longest distance are Precious Metals funds, Technology funds, REIT funds, Bond Funds, and Energy Funds.

When the small cap fund is the center, the five funds with largest distance are Technology funds, Precious Metals funds, Utilities Funds, Energy funds, REIT funds.

When the energy fund is the center, the five funds with biggest distance are Technology funds, Precious funds, Small Cap Growth funds, REIT funds, and Consumer funds.

When the utilities fund is the center, the five funds with the best distance are Precious Metals funds, Technology funds, REIT funds, Consumer funds, and Energy funds.

When the bond fund is the center, the five funds with the farthest distance are Precious Metals funds, Small Cap Growth funds, Mid Cap Growth funds, Consumer funds, and Industrial funds.

When the REIT fund is the center, the five funds with the best diversification are Technology funds, Precious Metals funds, Large Cap Growth funds, Small/Mid Cap Growth funds, and Utilities Funds.

Now we have concluded the one-dimensional study for the general styles and sectors funds. We are satisfied with the current results. Now we are prepared to study one family of funds. Now the Vanguard family is the largest one in the United States. So we are ready to study the Vanguard funds.

In the first round of study, we have selected 52 Vanguard funds with at least 10 years of records. We are looking for the best pairs of funds within this family of funds.