Market index investment

Instructions

Use the data in VLIFX.xls, which are monthly returns from January 1980 to March 2017 for Value Line’s Mid-Cap Focused Fund (VLIFX). This fund changed its name in recent years but is essentially the company’s first fund started in 1950. The return data are:

• VLIFX
• ExcessMarket (value-weighted market index minus the 1 month Treasury bill)
• SMB (small stocks’ return minus large stocks’ returns)
• HML (high BE/ME stocks’ return minus low BE/ME stocks’ return)
• UMD (return of last year’s highest-return stocks minus return of last year’s lowest-return stocks)
• RF (1 month Treasury bill return)

Value Line states that the VLIFX Fund “relies primarily on the rankings of companies by the Value Line Timeliness Ranking System (the Ranking System) in selecting securities for purchase or sale.” Value Line’s Ranking System has a well-known track record of predicting stock returns. (See the http://www.valueline.com/About/Ranking_System.aspx (Links to an external site.)Links to an external site. )

Here’s a summary of using the factor betas to determine investing style.

Question 1

If you invested $10,000 at the beginning of the sample period, what would the value of your investment have grown to by the end of the sample? Round to whole dollars. [Report as “$_ _ _, _ _ _”]

$10,000 invested in the Market index would have been valued at  , invested in VLIFX would have been valued at  .

Flag this QuestionQuestion 2

Calculate the geometric average annual return of the Market over the sample period, and calculate the VLIFX’s geometric average annual return. Report each in percentages, rounded to two decimal places, and without % sign.

The geometric average annual return of the Market is  , and the geometric average annual return of VLIFX is  .

(The Securities and Exchange Commission requires each mutual fund to compare their returns to the returns of a benchmark index in this way, as opposed to arithmetic averages.)

(1+rgeoavgannual)=(1+rfull?period)1NumberofYears

Flag this QuestionQuestion 3

The fund’s Market beta over the sample period is estimated to be  ______.  (Round to two decimal places.)

Flag this QuestionQuestion 4

The fund’s average monthly alpha based on the CAPM is _____ basis points.

Flag this QuestionQuestion 5

The estimated monthly CAPM alpha is significantly different from zero at the five percent level of significance.TrueFalse

Flag this QuestionQuestion 6

Three additional factors are given (which in this case are return anomalies). Test that each of the three has a return premium that is different from zero. Note that each factor is expressed in terms of a return premium, i.e. a long minus short portfolio. So you need to test the null hypothesis that the means of each factor — SMB, HML, and UMD — equal zero.

Which is the only factor with a mean that is not different from zero at the five percent level of significance over this sample period?

SMBHMLUMD Flag this QuestionQuestion 7

Estimate the fund’s mean monthly 4-factor alpha using the model below.

E(ri)=rf+?iME(rm?rf)+?isSMB+?iHHML+?iUUMD+?i

Report the alpha rounded to the nearest basis point.

Flag this QuestionQuestion 8

The 4-factor monthly alpha estimate is different from zero at the five percent level of significance. TrueFalse

Flag this QuestionQuestion 9

Test that the investing styles (factor betas) on SMB, HML, and UMD are respectively equal to zero at the five percent level of significance. VLIFX tended to invest in:

small-cap stock and value stockssmall-cap stocks, growth stocks and contrarian stockslarge-cap stocks and momentum stocksgrowth stocks and momentum stocksvalue stocks and momentum stocks

Flag this QuestionQuestion 10

The mean monthly return of the fund was 0.85%. How many basis points is attributable to the fund’s momentum strategy? Report your answer rounded to the nearest basis point.

Flag this QuestionQuestion 11

The fund currently charges an annual fee of 1.20% of assets under management. Estimate how many basis points per month are lost by the fund’s investors due only to the fees paid to the fund. (Just estimate by dividing by 12.  For comparison, some of the larger stock index funds charge fees under 10 basis points per year.)  Flag this Question

Question 12

Based on past performances alone (which I do not advise in practice), would you select the Value Line fund or the Market index to be your sole risky investment going forward? Explain. Assume that you can borrow or lend at the risk-free rate. Note that a new portfolio manager took over in 2009.

 
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