{"id":9127,"date":"2023-03-10T16:29:07","date_gmt":"2023-03-10T16:29:07","guid":{"rendered":"https:\/\/www.goodacademic.com\/blog\/questions\/use-python-to-solve-sml-four-factor-model-arima-forecasting-market-risk-and-volatility-problems\/"},"modified":"2023-03-10T16:29:07","modified_gmt":"2023-03-10T16:29:07","slug":"use-python-to-solve-sml-four-factor-model-arima-forecasting-market-risk-and-volatility-problems","status":"publish","type":"questions","link":"https:\/\/www.goodacademic.com\/blog\/questions\/use-python-to-solve-sml-four-factor-model-arima-forecasting-market-risk-and-volatility-problems\/","title":{"rendered":"use python to solve sml, four-factor model, arima forecasting, market risk and volatility problems"},"content":{"rendered":"
\n Learning Goal: <\/b>I’m working on a finance multi-part question and need the explanation and answer to help me learn.<\/p>\n

Instructions:<\/span>The assignment has to be submitted as a single pdf file (Python output (tables and graphs) followed by your comments and interpretations, merged with the Python script exported as a pdf output file),<\/span>together with data<\/span>sets<\/span>(as a <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

separate single Excel file).<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PART A: Descriptive Statistics, SML and Four-Factor Model.<\/span> (5 pts.)<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<\/span>
Problem A1.<\/span>
Download<\/span> data<\/span> for<\/span> any<\/span> three<\/span> stocks<\/span> and<\/span> corresponding<\/span> market<\/span> index<\/span> for<\/span> any<\/span> available<\/span> period<\/span> of<\/span> your<\/span> choice<\/span> from<\/span>
(YahooFinance).<\/span> The data set should include at least 252 observation, but there is no upper limit for the number<\/span>
of<\/span> observation.<\/span> Also,<\/span> your<\/span> data<\/span> set<\/span> (the<\/span> period<\/span> and<\/span> the<\/span> market<\/span> index)<\/span> should<\/span> remain<\/span> confidential.<\/span> Use<\/span> Python<\/span>
(exclusively)<\/span> to:<\/span> (a)<\/span> calculate<\/span> the<\/span> descriptive<\/span> statistics<\/span> (mean,<\/span> median,<\/span> variance,<\/span> standard<\/span> deviation,<\/span> skewness,<\/span>
kurtosis,<\/span> coefficient<\/span> of<\/span> variation)<\/span> for<\/span> both<\/span> the<\/span> stocks<\/span> and<\/span> the<\/span> index,<\/span> and<\/span> comment<\/span> on<\/span> the<\/span> observed<\/span> dynamics;<\/span> (b)<\/span>
develop and interpret the SML for each stock (plot all three on the same plot, comment on the intercept, the slope,<\/span>
their meaning, etc.).<\/span> The Python output and your comments\/interpretation should be included in the main pdf file.<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Problem A2.<\/span>
Download<\/span> data<\/span> for<\/span> 5<\/span> industry<\/span> portfolios<\/span> from<\/span> Keneth<\/span> R.<\/span> French<\/span> data<\/span> library<\/span> (Online<\/span> Data<\/span> Library),<\/span> and<\/span> corre-<\/span>
sponding<\/span> factors<\/span> and<\/span> risk-free<\/span> rate<\/span> (you<\/span> will<\/span> need<\/span> to<\/span> download<\/span> all<\/span> necessary<\/span> factors<\/span> for<\/span> this<\/span> assignment).<\/span> Data<\/span>
set<\/span> should<\/span> include<\/span> at<\/span> least<\/span> 252<\/span> observation,<\/span> but<\/span> there<\/span> is<\/span> no<\/span> upper<\/span> limit<\/span> for<\/span> the<\/span> number<\/span> of<\/span> observation.<\/span> Pick<\/span> any<\/span>
two<\/span> industry<\/span> portfolios<\/span> from<\/span> the<\/span> data<\/span> set<\/span> (out<\/span> of<\/span> those<\/span> 5<\/span> portfolios),<\/span> and<\/span> estimate<\/span> the<\/span> four-factor<\/span> model<\/span> for<\/span> each<\/span>
industry<\/span> portfolio<\/span> (two<\/span> models).<\/span> Comment<\/span> on<\/span> the<\/span> estimated<\/span> coefficients,<\/span> and<\/span> the<\/span> goodness-of-fit<\/span> for<\/span> each<\/span> model.<\/span>
The Python output and your comments\/interpretation should be included in the main pdf file.<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PART B: ARIMA Forecasting & Market Risk.<\/span> (15 pts.)<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<\/span>
Problem B1.<\/span>
Download data for S&P 500, Russell 2000, and Bitcoin for any available period of your choice from YahooFinance<\/span>
and CoinMarketCap.<\/span> The data set should include at least 252 observation, but there is no upper limit for the num-<\/span>
ber of observation.<\/span> Also, your data set should remain confidential.<\/span> Use Python (exclusively) to plot the distribution<\/span>
of log returns for these three assets.<\/span> Comment on the difference in the distribution of the returns, having in mind<\/span>
different risk-preferences (risk aversion vs.<\/span> risk loving investors).<\/span> The Python output and your comments\/interpre-<\/span>
tation should be included in the main pdf file.<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
<\/span><\/span><\/span><\/span>Problem B2.<\/p>\n

Specify<\/span> an<\/span> appropriate<\/span> ARIMA<\/span> model<\/span> (your<\/span> specification<\/span> must<\/span> be<\/span> justified<\/span> by<\/span> different<\/span> statistical<\/span> tests)<\/span> for<\/span> each<\/span>
time<\/span> series<\/span> and<\/span> forecast<\/span> the<\/span> log<\/span> returns<\/span> for<\/span> these<\/span> three<\/span> assets<\/span> 15<\/span> days<\/span> ahead.<\/span> Plot<\/span> the<\/span> forecasted<\/span> returns<\/span> for<\/span> each<\/span>
asset<\/span> and<\/span> comment<\/span> on<\/span> the<\/span> ARIMA<\/span> forecasting<\/span> output.<\/span> The<\/span> Python<\/span> output<\/span> and<\/span> your<\/span> comments\/interpretation<\/span>
should be included in the main pdf file.<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Problem B3.<\/span>
Use<\/span> Python<\/span> and<\/span> the<\/span> log<\/span> returns<\/span> for<\/span> these<\/span> three<\/span> assets<\/span> to<\/span> calculate:<\/span> (a)<\/span> the<\/span> VaR<\/span> (90%,<\/span> 95%<\/span> and<\/span> 99%<\/span> C.L.),<\/span> (b)<\/span>
backtesting<\/span> estimations<\/span> of<\/span> these<\/span> VaR<\/span> values;<\/span> (c) the<\/span> CVaR<\/span> (90%,<\/span> 95% and<\/span> 99%<\/span> C.L.).<\/span> Comment<\/span> on<\/span> the meaning<\/span>
and<\/span> the<\/span> dynamics<\/span> of<\/span> these<\/span> estimated<\/span> losses<\/span> for<\/span> each<\/span> asset<\/span> and<\/span> across<\/span> the<\/span> assets.<\/span> What<\/span> would<\/span> be<\/span> your<\/span> investment<\/span>
advice for different type of portfolio investors?<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PART C: Volatility (Historical Volatility & GARCH).<\/span> (15 pts.)<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<\/span>
Problem C1.<\/span>
Download data for any two stocks and any two cryptocurrencies for any available period of your choice from Yahoo-<\/span>
Finance and CoinMarketCap.<\/span> Use Python to:<\/span> (a) calculate and plot on the same chart the log returns for each of<\/span>
these assets; (b) plot the distribution of these log returns and comment on possible asymmetries and their meaning<\/span>
from the investment perspective.<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Problem C2.<\/span>
Calculate and plot any two measures of historical volatility for each asset (four plots, one for each asset).<\/span> Comment<\/span>
on the dynamics of historical volatility by comparing the trends (within and across the markets).<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Problem C3.<\/span>
Use<\/span> Python<\/span> to<\/span> estimate<\/span> GARCH<\/span> (1,1)<\/span> model<\/span> for<\/span> both<\/span> stocks<\/span> separately.<\/span> Comment<\/span> on<\/span> the<\/span> estimated<\/span> GARCH<\/span>
coefficients, and compare the estimated results obtained from these two models.<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Problem C4.<\/span>
Use<\/span> Python<\/span> to<\/span> estimate<\/span> GARCH<\/span> (1,1)<\/span> model<\/span> for<\/span> both<\/span> cryptos<\/span> separately.<\/span> Comment<\/span> on<\/span> the<\/span> estimated<\/span> GARCH<\/span>
coefficients,<\/span> and compare the estimated results obtained from these two models.<\/span> Also,<\/span> compare and comment the<\/span>
estimated GARCH coefficients for all four GARCH models.<\/span>
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . <\/p>\n

\u00e2\u20ac\u00a2<\/span> Use Python (exclusively) for each problem, export all tables, figures, and computational results to<\/span>
a docx file.<\/span>
\u00e2\u20ac\u00a2<\/span> Interpret and comment all the results according to the requirements written in each problem.<\/span>
\u00e2\u20ac\u00a2<\/span>Export Python script as a pdf file (it has to be organized to follow the problems in the assignment),<\/span>
and merge it with the main pdf file (the main file followed by the Python script) to make a single pdf file.<\/span>
\u00e2\u20ac\u00a2<\/span> Submit the single pdf file, together with a separate Excel file (that includes all data sets in different<\/span>
spreadsheets) exclusively through Canvas (so, you are supposed to submit only two files).<\/span>

<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\n

Requirements:<\/p>\n<\/p><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Learning Goal: I’m working on a finance multi-part question and need the explanation and answer to help me learn. Instructions:The assignment has to be submitted as a single pdf file (Python output (tables and graphs) followed by your comments and interpretations, merged with the Python script exported as a pdf output file),together with datasets(as a […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":[],"disciplines":[676],"paper_types":[],"tagged":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/9127"}],"collection":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/comments?post=9127"}],"version-history":[{"count":0,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/9127\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/media?parent=9127"}],"wp:term":[{"taxonomy":"disciplines","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/disciplines?post=9127"},{"taxonomy":"paper_types","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/paper_types?post=9127"},{"taxonomy":"tagged","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/tagged?post=9127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}