FINM8006 Advanced Investment Assignment Due 11/10/2024

Qiaoqiao Zhu

1 Chinese A-Share Market Stock market in China is often said to be heavily influenced by individual traders.Size and liquidity therefore are long suspected to play important roles in ChineseA-share market. Mutual fund industry has been developing in the recent years,especially after 2016. In this exercise, we will analyze the Chinese market from2012 to 2022.

1.1 Data Description The data folder contains two zipped (.gz) csv files.

• monthly_returns_cn.csv.gz contains monthly stock and market returnsfor stocks on Chinese market from 2010 to 2022.

– stkcd: stock code

– month: date of monthly end date

– ret: stock return

– mktret: market return– rf: risk free rate

• monthly_characteristics_cn.csv.gz contains firm characteristics ofthe shares traded each month from the market and earnings announcements.– stkcd: stock code– priormonth: end of the month date when characteristics information

is known

– market_value: market cap (value) of stock in the month

 ep: EP ratio calculated as earnings divided by market cap– amihud: average Amihud measure in a month. Amihud measure is ameasure of stock illiquidity, calculated as stock price change divided

by trading volume. The higher the value the lower a stock’s liquidity.

1.2 Your Tasks

11.2.1 Mean Variance

Suppose you inherited an amount of money (M) at the end of year 2020 and wantto invest it in a basket of stocks and risk free asset at the beginning of 2021.stkcds of the stocks in your basket are ['600519', '002594', '002415','000333'] 代 写FINM8006 Advanced Investment and the risk free rate is known at the beginning of 2021. You haveCRRA utility function of risk aversion 𝛾 = 3. You estimate the return characteristics using data in the last 3 years prior to 2021.

1. What is your optimal share of M to invest in the stock basket?
2. What is the optimal share of M to invest in each stock if you decide to domean-variance investing?

3. What are the returns you expected to get and you will actually get (fromM, consider only the stock returns) in January 2021?

4. If you compose your stocks in the basket based on their relative marketcaps at the end of 2020, what return (from M, consider only the stock

1.2.2 CAPM BETA

For each stock and month starting from January 2012, use the prior 24 monthto estimate CAPM 𝛽. You will require a firm-month to have at least 12 monthsof prior data to estimate, otherwise the firm-month will be dropped from theportfolio. From now on, your data will be firms with legitimate beta and othercharacteristics information.For each month starting from 2012, form 10 portfolios according to their CAPM

𝛽, then plot the average realized monthly excess return against the average 𝛽

for the 10 portfolios. Add the CAPM line also to your graph. Please comment

on the graph you produce, what kind of the stocks are likely to be overvalued

or undervalued.

1.2.3 Size and EP Ratio

For each month starting from 2012, form 25 (5x5) portfolios by sorting stocksaccording to size (proxied by market value) and EP ratio. Stock characteristicsin a month is its characteristics in the prior month. Calculate the value-weightedreturns and betas. Produce a within-size plot and a within-PE plot for the 25portfolios by plotting mean excess return against CAPM as in the lecture notes.Comment on your graphs.

1.2.3.1 Size and EP factors

You will divide your stocks into 6 (2X3) portfolios according to size and EP.Returns in the portfolios are value-weighted. Then you will form your SMB(size) factor by longing the equally-weighted portfolios of small stock portfolios2and shorting the equally-weighted portfolios of big stock portfolios, form yourHML (EP) factor by longing the equally-weighted portfolios of high EP stock

portfolios and shorting the equally-weighted portfolios of low EP stock portfolios.

Plot the cumulative factor returns along with the cumulative market excessreturn.Run multi-factor models of market excess return, SMB and HML for each of the25 portfolios you formed earlier, and get the factor loading. Produce within-sizeand with-EP plots by plotting average portfolio excess returns against averagemodel predicted excess returns. You get model predicted excess returns fromfactor loading and mean factor returns. Has the multi-factor loading improved

the model prediction?

1.2.4 Liquidity Premium

Is there liquidity premium and What is its dynamics? Let’s examine. In addition to the 2X3 sorting, we also sort independently into 5 portfolios accordingto amihud. That is, we sort stockings into 2X3X5 portfolios of size, EP andliquidity. Again, portfolio returns are value weighted. Finally, we form liquidity premium by longing the equally-weighted portfolios of high illiquiditystock portfolios and shorting the equally-weighted portfolios of low illiquidity

stock portfolios. Calculate the time-series of liquidity premium, and plot thecumulative returns of the premium. Comment on the graph you get.

1.3 Python Notes

You can use pandas to read zipped csv files. Notice that stkcd is a str, andmonth is a date, they need to be specified in reading to have the correct dataype, such as the following:monthly_returns = pd.read_csv('monthly_returns_cn.csv.gz',parse_dates=['month'], dtype={'stkcd':'str'})

You will need statsmodels for regression. For rolling regression, you can usea for loop as the backtesting workshop, or use RollingOLS in statsmodels.To calculate things by group, the groupby method of pandas will be useful.You can use apply following groupby to get results in a new data frame, or usetransform to add the results to the existing dataframe. Please see lecture notesand pandas documentation online for details.qcut method of pandas is handy for finding the cutoff and sorting dataframeinto groups. The following lambda function, when applied to x, put 10 grouplabels, size0…size9 according to x.lambda x: pd.qcut(x, 10, labels=['size'+str(x) for x in range(10)], retbins=False)3