1. QF302 Consumer Non-Cyclicals
Damian Ang Wei Jie, Lim Song Eng, Wang JiaHui, Xu Leyi

2. AGENDA Introduction Risk Measures Analysis ETFs Ranking
Minimum Variance Portfolio
Conclusion

3. 1
Introduction

4. Good for Hedging: Consumer Non-Cyclical Goods
The Non-Cyclical Consumer Goods and Services economic sector consists of companies engaged in fishing and farming operations; the processing and production of food, beverages and tobacco; manufacturers of household and personal products; and providers of personal services.
The non-cyclical securities, also called defensive stocks, experience profit regardless of economic gyrations because they produce or distribute goods and services we always need: food, power, water and gas.

5. ETFs & Respective Strengths
Momentum: PSL
Market Cap: FSTA, IYK, PSCC, XLP
Replicates > 90% of index, which has about 30 “high-momentum” common stocks
> 70% exposed to Consumer Staples
Main industries are food, beverages, households and consumer services
Tends to be more stable given concentrated investments in large-cap companies
Largely favour large-cap firms: FSTA(89%), IYK (97%), XLP(80%)
Fan of small-cap:PSCC (90%)
Multifactor: FXG
Equal weighted: RHS
Chosen based on a mix of attractive attributes such as cheap valuation, high dividend yield, high quality, positive momentum, and/or low volatility.
> 80% on large- + mid-cap firms
Main industries are food and food staples
Closely tracks an unmanaged equal weighted version of the S&P 500 Consumer Staples Index
>87% in large-cap firms

6. 2 Risk Measures Analysis

7. Risk Measures Sharpe Ratio Treynor Ratio Jensen’s Alpha
Fama-French Market Beta
Skewness & Kurtosis
R-squared
Information Ratio
Variance Ratio Test

8. Sharpe Ratio 𝑆𝑅= 𝑟 𝑖 −𝑟 𝜎 𝑖
Measure of stock or fund reward to risk ratio
Ratio of an asset’s excess return to its volatility
Can be computed either ex- ante or ex-post
𝑆𝑅= 𝑟 𝑖 −𝑟 𝜎 𝑖
𝑟 𝑖 =𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑎𝑠𝑠𝑒𝑡
𝑟=𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘
𝜎 𝑖 =𝑆𝐷 𝑜𝑓 𝑟 𝑖
A higher Sharpe metric is always better than a lower one because a higher ratio indicates that the portfolio is making better investment decisions and not being swayed by the risk associated with it.

9. Sharpe Ratio Sharpe Ratio Ranking FSTA 0.0969 7 RHS 0.0741 6 XLP
0.0257 5
PSCC
0.0138 4
PSL
0.0116 3
FXG 2
IYK 1

10. Treynor Ratio 𝑇𝑅= 𝑟 𝑖 −𝑟 𝛽 𝑖 Similar to Sharpe Ratio
Uses systematic risk Beta computed from CAPM instead
Adjust all investments for market volatility and the risk associated with it in an effort to compare investments based on their performance instead of market factors
𝑇𝑅= 𝑟 𝑖 −𝑟 𝛽 𝑖
𝑟 𝑖 =𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑎𝑠𝑠𝑒𝑡
𝑟=𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘
𝛽 𝑖 =𝑠𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑟𝑖𝑠𝑘 𝑜𝑓 𝑟 𝑖
Investors and analysts use this calculation to compare different investment opportunities’ performance by eliminating the risk due to volatility component of each investment. By canceling out the affects of this risk, investors can actually compare the financial performance of each fund or investment.
For example, one fund manager might make better investment decisions for long-term profitability, but another fund outperforms it in the short run because of market up and down swings. The Treynor calculation cancels out this market instability to show which fund manager is actually making better decisions and creating a fundamentally more profitable investment.

11. Treynor Ratio Treynor Ratio Ranking PSCC 0.4978 7 IYK 0.4420 6 PSL 5
XLP 4
FXG 3
RHS 2
FSTA 1

12. Jensen’s Alpha
Determine abnormal return of a financial asset or portfolio
Positive alpha is synonym of abnormal return
𝛼 𝐽 = 𝑟 𝑖 − 𝑟+ 𝛽 𝑖 𝑅 𝑚 −𝑟
𝑟 𝑖 =𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑎𝑠𝑠𝑒𝑡
𝑟=𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘
𝛽 𝑖 =𝑠𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑟𝑖𝑠𝑘 𝑜𝑓 𝑟 𝑖
𝑅 𝑚 =𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑟𝑒𝑡𝑢𝑟𝑛

13. Jensen’s Alpha Jensen’s Alpha Ranking RHS 0.0720 7 FSTA 0.0714 6 XLP
0.0310 5
PSL
0.0140 4
PSCC
0.0079 3
IYK 2
FXG 1

14. Fama-French Market Beta
Asset returns are not entirely dependent on market beta as proposed by CAPM.
FF3 decomposes CAPM Beta into multiple factor Betas (market cap Beta and value Beta)
𝑟 𝑖 = 𝑟 𝑓 + 𝛽 1 𝑟 𝑚 − 𝑟 𝑓 + 𝛽 2 𝑆𝑀𝐵 + 𝛽 3 𝐻𝑀𝐿 +𝜀

15. Fama-French Market Beta
Ranking
FXG
0.0108 7
FSTA 6
PSL 5
PSCC
0.0297 4
IYK 3
RHS 2
XLP 1

16. Skewness Rule of thumb in interpreting skewness:
|skewness|>=1:Distribution is highly skewed
0.5<|skewness|<1:Distribution moderately skewed
|skewness|<0.5:Distribution is approximately symmetrical
If 𝑍 𝑔1 <−2,the population is very likely negatively skewed
If −2≤𝑍 𝑔1 ≤2, can’t reach any conclusion about the skewness of the population
If 𝑍 𝑔1 >2,the population is very likely positively skewed
This is an interpretation of the data you actually have. When you have data for the whole population, that’s fine. But when you have a sample, the sample skewness doesn’t necessarily apply to the whole population. In that case the question is, from the sample skewness, can you conclude anything about the population skewness?
𝑡𝑒𝑠𝑡 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐: 𝑍 𝑔1 = 𝐺 1 𝑆𝐸𝑆 , where SES= 6𝑛(𝑛−1) (𝑛−2)(𝑛+1)(𝑛+3)

17. Kurtosis A normal distribution has kurtosis exactly 3
Excess kurtosis = sample kurtosis- 3
If 𝑍 𝑔2 <−2,the population very likely has negative excess kurtosis
If −2≤𝑍 𝑔2 ≤2, can’t reach any conclusion about kurtosis
If 𝑍 𝑔1 >2,the population very likely has positive excess kurtosis
𝑡𝑒𝑠𝑡 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐: 𝑍 𝑔2 = 𝐺 1 𝑆𝐸𝐾 , where SEK=2(𝑆𝐸𝑆) 𝑛 2 −1 (𝑛−3)(𝑛+5)

18. Skewness & Kurtosis Excess Kurtosis Skewness Ranking FSTA -3.5886 7
PSCC 6
RHS
3.0676 5
XLP
8.2815 4
IYK 3
PSL 2
FXG 1

19. R2
A statistical measure of how close the bi-weekly returns of ETF are to the bi-weekly returns of the corresponding index.
R2 close to 1
→ Strong correlation to the index
𝑅 2=1− 𝑅𝑆𝑆 𝑇𝑆𝑆
𝑅𝑆𝑆=𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠
𝑇𝑆𝑆=𝑇𝑜𝑡𝑎𝑙 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠

20. R2 R2 Ranking FSTA 0.9831 7 XLP 0.9814 6 PSCC 0.9805 5 RHS 0.9775 4
FXG
0.9657 3
IYK
0.9485 2
PSL
0.7464 1

21. Information Ratio
A ratio of ETF return above the index return to the volatility of the returns
Higher information ratio
→ Outperforms the index
𝐼𝑛𝑓𝑜 𝑅𝑎𝑡𝑖𝑜= 𝔼 𝑟 𝑝𝑡 − 𝑟 𝑏𝑡 𝜎( 𝑟 𝑝𝑡 − 𝑟 𝑏𝑡 )
𝑟 𝑝𝑡 =𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑎𝑠𝑠𝑒𝑡
𝑟 𝑏𝑡 =𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘

22. Information Ratio Info Ratio Ranking PSL -0.0048 7 FXG -0.0157 6 PSCC 5
IYK 4
RHS 3
FSTA 2
XLP 1

23. Random Walk Variance Ratio Test
VR(q)=1 when log returns are serially uncorrelated and homoscedastic
Z(10)
→ Deviation from 0
𝑡𝑒𝑠𝑡 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐:
𝑍 𝑞 = 𝑀 𝑞 𝐽 𝑟 (𝑞) 2(𝑞−1)

24. Random Walk Z(10) Ranking XLP -5.483 7 IYK -5.064 6 PSL -4.65 5 FXG
-3.988 4
PSCC
-3.233 3
RHS
-1.666 2
FSTA
-0.718 1

25. 3
ETFs Ranking

26. ETFs Ranking Total Rank Points Overall Ranking PSCC 37 7 FSTA XLP 33 5
PSL 32 4
RHS 31 3
IYK 27 2
FXG

27. Long/Short Strategy
Take into consideration of both ranking and capital requirement
Price
Overall Ranking
Long/Short
Cashflow
PSCC
66.40 7
Short
FSTA
31.48
Long
-31.48
XLP
52.18 5
-52.18
PSL
55.03 4
RHS
120.13 3
IYK
113.36 2
FXG
45.37
Total
76.37

28. 4 Minimum Variance Portfolio
The X Factor

30. Correlation Matrix 819 daily values
Assume correlations are stable over time

31. Solve for Minimum Variance
Weights
Quadratic Programming
Returns & Correlations
(cvxopt Library)

32. Outcomes Expected 2-Week Return: 0.73% Actual 2-Week Return: 6.09%
2-Week Volatility: 1.95%
Could be because of US bull market since Trump became President
Sometimes markets are irrational

33. Limitations
Only consider variance and covariance an no comparison with market and index
Assume that correlations are stable over time
Distribution of returns might not be normal

34. 5
Conclusion

35. Remember Day 0? Price Overall Ranking Long/Short Cashflow PSCC 66.40 7
FSTA
31.48
Long
-31.48
XLP
52.18 5
-52.18
PSL
55.03 4
RHS
120.13 3
IYK
113.36 2
FXG
45.37
Total
76.37
Excess Cash = 76.37
Margin Deposit

36. Part 2 of Day 0 Re-invest into long positions Pray. Pray hard. Price
Overall Ranking
Long/Short
Cashflow
Add-on Investment
Shares Owned
PSCC
66.40 7
Short - -1
FSTA
31.48
Long
-31.48
-11.80
1.37
XLP
52.18 5
-52.18
-19.55
PSL
55.03 4
RHS
120.13 3
-45.02
IYK
113.36 2
FXG
45.37
Re-invest into
long positions
Pray.
Pray hard.

37. 2 Weeks Future Returns Great (4-7) PSCC (66.53 -> 68.53) 3.01%
FSTA( >33.01 ) 4.17%
XLP ( > ) 4.37%
PSL( > 56.9) 3.32%
Can Be Better (<4)
RHS( > ) 3.84%
IYK( > ) 4.28%
FXG( >46.7) 2.91%

38. Day 14 Day 14 Prices Price Overall Ranking Long/Short Cashflow (Day0)
Add-on Investment
Shares Owned
(Day14)
PSCC
68.53 7
Short
66.40 - -1
-68.53
FSTA
33.01
Long
-31.48
-11.80
1.37
45.38
XLP
54.96 5
-52.18
-19.55
75.56
PSL
56.90 4
55.03
-56.90
RHS
126.30 3
-45.02
173.58
IYK
118.70 2
113.36
FXG
46.70
45.37
-46.70
Total
3.69
Day 14 Prices

39. Day 15 But… Same day transactions No (obscene) transaction costs
We need $10 million
Still,
Thank you for your time

40. Thank You!
ANY QUESTIONS?