Investment Analysis: CAPM

Anh Nguyen
Oct 6, 2021
3 min read

Updated: Dec 17, 2021

Investment Analysis #4

Prepared by Anh Nguyen

Instructed by Dr. Jay Chen

It is better off for investors to diversify their portfolio by considering other ETFs such as QQQ and GLD instead of investing only in SPY. Diversifying the portfolio could yield a better return than the market portfolio and more consistently positive abnormal returns. (Chen, 2020, p.18). In this report, I will analyze monthly returns from September 2019 to August 2021 of SPY, QQQ, GLD, and mixed portfolios using Sharpe ratio (the reward to total risk ratio) and Treynor's measure (the reward to systematic risk ratio) to pick out the best option for your money.

Background information:

QQQ is one of the most popular exchange traded funs (ETF) that tracks 100 largest technology companies like Apple, Amazon, Facebook, Google. GLD is the ticker of SPDR Gold Shares ETF tracking the price of a tenth of an once of gold. GLD is sponsored by World Gold Trust Services, LLC. QQQ is traded on Nasdaq and GLD is traded on NYSE; both of ETFs are sorted or invested the same way as other stocks do (Prospectus SPDR, 2020).

Using Google Sheet, I could pull out the monthly return series of three ETFs between September 2019. The table 1 shows three stocks' mean monthly returns, standard deviations and Sharpe ratios, assuming that the risk free rate to be 0.1% per month. The detailed calculation is attached here.

Table 1:

	SPY	QQQ	GLD
Mean monthly return	0.0120	0.0169	0.0006
Standard deviation	0.0444	0.0361	0.0450
Sharpe ratio	0.8621	1.5232	-0.0298

Over the time, QQQ yields the highest average monthly return. QQQ also holds the least total risk with the smallest standard deviation and highest reward to total risk ratio . QQQ is the most potential stock for your money out of three based on the given data. GLD generates the lowest reward as it has the highest total risk and lowest average monthly return. SPY is the safe option with a decent average monthly return and good reward over total risk.

Estimate β and Treynor’s Measure:

Use the same data as above and consider SPY as the market portfolio, I could create a table 2 for SPY, GLD, and QQQ's Treynor' measures. Treynor's measure is the reward to systematic risk ratio. It is measured by having average monthly return after deduction from risk free rate divided by the systematic risk of a security, which is stock's estimated beta. The detail for calculation is attached here.

Table 2:

	SPY	QQQ	GLD
Beta	1	0.2471	0.0644
Treynor's measure	0.0110	0.0642	-0.0059

Based on table 2, investors in QQQ hold a higher systematic risk securities but are rewarded with higher returns than the market portfolio. The trend is opposite for GLD. Investors in GLD are rewarded with lower returns and hold a lower systematic risk securities.

Portfolio Management:

I will create a Portfolio X mixing GLD and QQQ to yield a desired beta of 1.5 and a Portfolio Y mixing GLD and QQQ to yield a desired monthly expected return of 1%. The result in in the table 3 and detail for calculation is attached here.

Table 3:

Portfolio X
X_GLD
-6.8578	7.8578
Return_P	Beta_P	Treynor's measure
0.1283	1.4999	0.0849
Portfolio Y
X_GLD	X_QQQ
0.4281	0.5719
Return_P	Beta_P	Treynor's measure
0.0099	0.1689	0.05274

Portfolio X yields 12.8% average monthly return given the desired beta of 1.5. Investors need to short heavily GLD and invest heavily on QQQ in the first portfolio. Portfolio Y has a much lower systematic risk beta of 0.168 given the desired average monthly return of 1%. Investors invest both in GLD and QQQ with more weights on the later stock.

Although there are big gaps in returns and betas, the rewards of Portfolio X and Portfolio Y are not so different. Portfolio X has a reward to systematic risk ratio of 0.0849 and Portfolio Y yields an amount of 0.05274. The Portfolio 1 is recommended for investors want to earn the highest return and can bear a much higher systematic risk of securities. Another safeer recommendation is to invest solely in QQQ.

Abnormal Returns and Information Ratio:

I will analyze Berkshire Hathaway (ticker: BRK-A) to test its abnormal returns and consistency of average returns. BRK is an American multinational conglomerate holding company, famous for its control and leadership by Warren Buffett. BRK has a diverse range of business with early focus on long term investment (Wikipedia, n.d.). Using Google Sheet, I could pull out data and create table 4:

BRK
Alpha	0.0088
Beta	0.2222
P-value	0.0019
Information ratio	0.2609

The alpha represents the the real monthly average turn of BRK of 0.0088 which is relatively good. Its systematic risk is also low. However, the information ratio indicates that the consistency of return is not just average, not good. Based on alpha and the information ratio, I could conclude that Buffett's reputation is not well justified.