Problem 4.4.

Introduction

The CAPM model can be used to analyze the performance of a portfolio of investments. The model should be calculated by comparing the return of assets (Ri) minus the return of risk-free cash (Rf) of the fund against those numbers of a known index with historical data (Rm). With least-squares regression, a straight line has to be drawn through the points to finish the model. Alpha represents the point where the graph starts and beta the slope of the regression line. Alpha is the number that represents the fact of how well the fund did against the CAPM model. A positive alpha means the fund did better than CAPM predicted and negative the opposite. R² represents the ‘fit’ of the model, so how much of the data fits the straight line.

(a) Al thinks that the estimated alpha is too high because of survivor bias. This concern is valid. This is due to several reasons. First, the R² presented is relatively low as the model fits only 32%. This means that 68% of the data is not explained by the model. Another point is the height of alpha. The monthly Sand Hill Index shows an average alpha in % per year of 4.92 at the significance level of 1, 5 and 10% level. The quarterly CA Index shows an alpha of 6.1 in % per year. According to the book ‘Venture capital and the Finance of Innovation (Wiley, 2010), these are lower and upper bounds of abnormal gross returns. The CA Index is considered an upper bound as the method of data collection of the Index is already considered having survivor bias. If we consider the fact that 5,73 and 6,1 are lower and upper bounds in the period of 1989 – 2008 plus given the fact that the financial crisis hit in 2008, the height of alpha = 7,5 could be considered as a concern. Furthermore, Largeco calculates their returns on the VC portfolio by adding the cash-flows and the reported company values from their funds. In the 10 years that Largeco operated (2006 – 2016), companies dropped out of their portfolio (due to failure). These companies do not report anything anymore and are therefore excluded from the reports (reported company values). Because of this, only the survivors are used to calculate the VC portfolio performance. This makes the performance biased upwards, because only the companies that survived for 10 years are considered. We can conclude that Al’s concern is correct and that it is indeed possible that alpha is too high due to survivor bias. Overcoming survivor bias is difficult. What perhaps should be done is calculating the performance twice, first according to the Sand Hill Index method (then you have the lower bound) and then according to the method used in the CA index. When both are significant, you have a range in which the correct alpha must be in.

(b) Bonnie thinks that the estimated beta is too low because of a stale value problem. This concern is valid. According to historical data from 1989 – 2008 of the Sand hill Index and CA Index, the market beta should be within 0.56 – 0.81. Therefore making 0.75 a relatively high estimate. With the interpretation of the results of the Sand Hill Index and CA Index, there are three problems. One of the three problems is the stale value problem. The stale value problem is referred to as using very old information to estimate values for unrealized investments. The stale value problem causes beta estimates to be biased downwards, unexplained returns are ‘credited’ to alpha which would be biased upwards by that. From the historical data of 1989 – 2008, an alpha of 0.75 would be expected to be good or a little too high instead of too low, therefore the concern is moderate. Still, taking into account that there is also an upward bias in alpha, the stale value problem could be an issue. Overcoming this can be done by adjusting the regression for all the interpretation problems: stale values, liquidity risk and style adjustments. To do so, past values must be included on the...