Question

There is a famous application of regression analysis in finance known as Capital Asset Pricing

Model (CAPM) formulated by Nobel Laureate William Sharpe. This model relates the rate of
return of a given security (a security or a mutual fund) to rate of return of market as a whole
and a risk free interest rate. The relationship is expressed as
ri − rf = β(rM − rf)
where ri is the rate of return of a given security (security or mutual fund), rM is the rate of
return of the overall market (for instance the S&P index), and rf is the risk free interest rate
(for example, ten-year treasury bills rate). The coefficient β is a measure of "riskiness" of the
security. If β > 1 then the security is riskier than the general market; if it is smaller than 1,
then it is less risky.
For this project you have to do some on-line research. Go on-line and obtain the daily clos-
ing for the last year, form October 6, 2022 to October 4, 2023 for securities: S&P 500 in-
dex ("ˆ GSPC"), ten-year treasury bond mutual fund ("ILBT"), Microsoft ("MSFT"), Apple Magellan you need to look at net asset value in place of closing price.
2a) Download closings of each security for the period given above and collect them into a data
frame called closings. One way is to download each security’s data separately and then
transfer the column under Adj. Close into a new *.csv file. If you choose this method,
make sure that the data are all aligned the same way in terms of date (some days, in
one security may have data, while anther may Make sure to submit your homework
assignment with this file.
Another, more elegant way is to read the data directly from the Yahoo site from your
R script, collect the data under the Adj.Close column, and collect them into your data
frame. If you use this method, you will not need any extra files.
Next, create a second data frame called returns and compute for each asset its daily
returns. Make the market return, that is S&P 500 the first column of returns. Recall the top ten and bottom ten rows of each
data frame.

Answer 1

The CAPM in finance relates security returns to market returns and risk-free rates; it uses β to measure riskiness. Investments are chosen based on expected returns, risk, and liquidity. Supply of financial capital shifts according to the changing preferences of investors over risk and return of various investments.

Step-by-step explanation:

The Capital Asset Pricing Model (CAPM) is an application of regression analysis in finance that relates the rate of return of a security to the market's rate of return and a risk-free interest rate. The model measures the riskiness of a security using the coefficient β, which compares the security's performance to the market as a whole. A β greater than 1 indicates that the security is riskier than the market, while a β less than 1 suggests it is less risky.

Individuals or households supplying financial capital need to understand the expected rate of return, risk, and actual rate of return for various investment options like bank accounts, bonds, stocks, and mutual funds. Expected rate of return represents the average earnings an investment is likely to generate over a certain period, while risk measures the likelihood that returns may diverge significantly from what's expected. The actual rate of return, on the other hand, is the total earnings on an investment over a time period, including both capital gains and interest.

Investment decisions often involve trade-offs between the potential returns and the associated risks. High-risk investments usually command higher expected returns to compensate for the increased uncertainty. Conversely, investments with lower risk tend to offer more stable but potentially lower returns. Investors' preferences for various investments will affect the supply of financial capital, shifting in response to changes in perceived risk and returns.