Statistics for investing (3.2) Joe's retirement plan invests in stocks through an "index fund" that follows the behavior of the stock market as a whole, as measured by the Standard & Poor's (S&P) 500 stock index. Joe wants to buy a mutual fund that does not track the index closely. He reads that monthly returns from Fidelity Technology Fund have correlation $r=0.77$with the $\mathrm{S}\&\mathrm{P}500$index and that Fidelity Real Estate Fund has correlation role="math" localid="1649424494964" $r=0.37$with the index.

(a) Which of these funds has the closer relationship to returns from the stock market as a whole? How do you know?

(b) Does the information given tell Joe anything about which fund has had higher returns?

Step by step solution

01

Part (a) Step 1: Given Information

Fidelity Technology Fund have correlation $r=0.77$

Fidelity Real Estate Fund has correlation $r=0.37$

Stock Index$=S\&P\left(500\right)$

02

Part (a) Step 2: Explanation

Relationships are closer if the linear correlation coefficient $r$is greater. For example, the fund "Fidelity Technology Fund" has a closer relationship than the fund "Fidelity Real Estate Fund".

03

Part (b) Step 1: Given Information 

Fidelity Technology Fund have correlation $r=0.77$

Fidelity Real Estate Fund has correlation $r=0.37$
Stock Index $=S\&P\left(500\right)$

04

Part (b) Step 2 : Explanation

There is no information regarding the size of the returns (value) since we only have linear correlation coefficient $r$.

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