1. Portfolio Analysis and Efficient Markets

2. Measuring Portfolio Risks
For individual securities, one thinks of risks as the standard deviation of its returns.
When we combine two or more securities into a portfolio (diversify), portfolio risk is related to that of the individual securities depending upon their correlation coefficient.
For two securities, say gold and Infosys, the risk of a portfolio will depend upon:
a) the proportion of funds invested in each (portfolio weights, W)
b) the individual risks of each (s).
b) the correlation between the two (rho).
As we talked about earlier, the search for low correlations has what has kept
money sloshing around the globe.
Correlations range from -1 (perfect negative) to +1 (perfect correlation). Discuss bonds and stocks, stocks and commodities, inter- and intra-industry connections.

3. The power of diversification
Just randomly picking stocks gets rid of 60% of the risk of the typical individual security by naive diversification
Most of the diversifiable risk eliminated at 25 or so stocks
6-3

4. E(r)
13% 8%
A=12%
B=20%
St. Dev
TWO-SECURITY PORTFOLIOS WITH DIFFERENT CORRELATIONS
WA = 0%
WB = 100%
r = -1
r = +1
r = .3
50%A
50%B
Complicated graph, but hopefully it will help.
Imagine two securities 1. Expected return is 8% and SD is 12%
2. Expected return is 13% and SD is 20%
Depending on the amount of correlation in the returns when we combine them we will alter the portfolio standard deviation. If there is perfect correlation the combination of the two securities has no diversification effects. However if the assets are perfectly negatively correlated we can combine the two securities to completely eliminate variance in the combined portfolio. Generally assets will be somewhere in between where the combination can eliminate some risk but not completely remove it.
WA = 100%
WB = 0%
6-4

5. Minimum Variance Combinations -1< r < +1
Choosing weights to minimize the portfolio variance 1 2
- Cov(r1r2) W1 = +
- 2Cov(r1r2) W2
= (1 - W1)
s 2
One question of interest is: With a given level of correlation how can we find the optimal weights of the securities so that we can minimize the variance of the portfolio. It turns out that we can solve for those weights using these equations.
Recall that Covariance(r1,r2) = 1,212
6-5

6. Extending to All Securities
Consider all possible combinations of securities, with all possible different weightings and keep track of combinations that provide more return for less risk or the least risk for a given level of return and graph the result.
The set of portfolios that provide the optimal trade-offs are described as the efficient frontier.
The efficient frontier portfolios are dominant or the best diversified possible combinations.
All investors should want a portfolio on the efficient frontier.
Dominant means they provide the best return for the given risk level.
… Until we add the riskless asset
6-6

7. The minimum-variance frontier of risky assets
Efficient Frontier is the best diversified set of
investments with the highest returns
Efficient
frontier
Found by forming portfolios of securities with the lowest covariances at a given E(r) level.
Individual
assets
Global
minimum
variance
portfolio
Minimum
variance
frontier
Individual assets combining them into portfolios, considering different weights.
So looking at many risky assets using the same techniques it is possible to build a minimum variance frontier. We are only concerned with the upper portion of the curve. Any minimum variance point on the bottom of the curve can be dominated by the similar point on the upper portion of the curve.
St. Dev.
6-7

8. The EF and asset allocation
E(r)
EF including international & alternative investments
Efficient
frontier
100% Stocks
80% Stocks
20% Bonds
60% Stocks
40% Bonds
40% Stocks
60% Bonds
Ex-Post
20% Stocks
80% Bonds
Alternative investments: REITs, mortgage backed, gold, other precious metals, other commodities and then the international investments.
100% Stocks
St. Dev.
6-8

9. ALTERNATIVE CALS s E(rP) CAL (P) P E(rA) A CAL (A) E(r) P&F
Efficient Frontier
P&F
E(rP&F)
CAL (Global
minimum variance) G P
There will only be one optimal Capital Allocation Line. This line will be the line that passes through the risk free rate at 0 SD and is tangent to the efficient frontier. It will dominate all other Capital Allocation Lines. F
Risk Free s A
6-9

10. The Capital Market Line or CML
CAL (P) = CML
E(r)
Efficient Frontier
E(rP&F)
The optimal CAL is called the Capital Market Line or CML
The CML dominates the EF P
E(rP)
E(rP&F)
There will only be one optimal Capital Allocation Line. This line will be the line that passes through the risk free rate at 0 SD and is tangent to the efficient frontier. It will dominate all other Capital Allocation Lines. F
Risk Free s
P&F P
P&F
6-10 10

11. The Capital Market Line or CML
CAL (P) = CML
E(r)
Efficient Frontier
E(rP&F)
The optimal CAL is called the Capital Market Line or CML
The CML dominates the EF P
E(rP)
E(rP&F)
There will only be one optimal Capital Allocation Line. This line will be the line that passes through the risk free rate at 0 SD and is tangent to the efficient frontier. It will dominate all other Capital Allocation Lines. F
Risk Free s
P&F P
P&F
6-11 11

12. Efficient frontier for international diversification
6-12

13. MUTUAL FUNDS IN INDIA
US HAS 9400 FUNDS, $19 TRILLION AS AUM, 45% IS EQUITY, 20% IS BONDS
INDIA SAVINGS RATE AT 30% OF GDP (SIMILAR TO KOREA, THAILAND, INDONESIA).
WHERE TO GO?
FIRST WAS UTI IN 1963, AMFI LISTS FIVE PHASES (BIT TOO MANY)

14. : UTI, 6700 CRORES AS OF 1987
PUBLIC SECTOR BANKS START MFS
PRIVATE SECTOR MUTUAL FUNDS
BLUES FROM GFC, ABOLISH FRONT-END LOADS
2014-NOW HAPPY DAYS ARE HERE AGAIN!

15. WHAT AMFI TELLS US.
Assets Under Management (AUM) as on December 31, 2018 stood at ₹22,85,912 crore. (income funds and liquid/money market is more than half…)
The AUM of the Indian MF Industry has grown from ₹ 4.13 trillion as on to to ₹22.86 trillion as on , about 5 ½ fold increase in a span of 10 years!!
Doubled in the first 5, to ₹8.26 trillion as on , then tripled in the next 5 to ₹22.86 trillion. MF SAHI HAI !!!
The # of folios at 80.3 million, retail is 67.6 million. This is 55th consecutive month witnessing rise in the no. of folios. (is this because this is the land of reincarnation!).

16. STILL WARY OF EQUITIES !!
SOME HINTS OF SIP ENROLLMENT DECLINES….

17. THUS FAR, YOU HAVE BEEN FAMILIAR WITH
a) EQUITY FUNDS (at least 65%); b) ELSS (at least 80%, tax break);, c) SECTOR/THEMATIC (tech, pharma), d) ETFs. w).
NOW FIVE BROAD GROUPS:
Equity, Debt, hybrid, Solution-Oriented (education, retirement, marriage, lock-in, decreasing exit loads), Other
AMC’s can generally have only one scheme in each category
Definition of large/mid/small-cap clarified.

18. EFFICIENT MARKETS
Random walks: no predictable pattern in stock prices.
Q: What if prices were predictable?
A: They would adjust immediately (who would wait around).
So, market prices should reflect available information.
Q: Why do prices move then?
A: must move when there is new (unexpected) information.
Q: Is new information predictable?
A: Would expect new information to be random (some good, some bad)
So, would expect deviations of prices from true value to be random (say about 1/3 of stocks overpriced, 1/3 under, 1/3 fairly priced…)
THIS IS WHAT IS MEANT BY MARKET EFFICIENCY.

19. EFFICIENT MARKETS - 2
Q: If markets are efficient, why search for stocks ?
THE NOTION OF EFFICIENT MARKETS IS A HYPOTHESIS.
TO CHECK IT, YOU TEST WHAT TYPES OF INFORMATION IS REFLECTED IN MARKET PRICES
• Markets are weak-form efficient IF information from trading data such as
past price and volume is reflected in prices (i.e what technical analysts do).
• Markets are semi-strong form efficient IF all public info, (trading + fundamental) is
reflected in prices. (i.e what fundamental analysts do).
• Markets are strong form efficient IF all info (public + private) is reflected in prices.

20. IMPLICATIONS OF THE EFFICIENT MARKET HYPOTHESIS (EMH).
If prices reflect available information and new information affects prices randomly THEN you wouldn’t expect investors to generate risk-adjust alpha’s consistently. A: Technical analysis Technical analysts look at past trading data, prices, volumes, odd lots, short interest etc to develop trading strategies. IF these trading strategies are successful (i.e they generate positive risk adjusted alpha) => markets not efficient in the weak form.

21. IMPLICATIONS OF THE EFFICIENT MARKET HYPOTHESIS (EMH).
If prices reflect available information and new information affects prices randomly THEN you wouldn’t expect investors to generate risk-adjust alpha’s consistently. B: Fundamental analysis. Fundamental analysts look at financial statements, earnings, dividends, interest rates, risk etc., and develop fair values for stock prices based on some sort of DCF or relative value analysis. IF their trading strategies are consistently successful THEN markets are not efficient in the semi-strong form.

22. IMPLICATIONS OF THE EFFICIENT MARKET HYPOTHESIS (EMH).
If prices reflect available information and new information affects prices randomly THEN you wouldn’t expect investors to generate risk-adjust alpha’s consistently C: Portfolio manager, insiders and others with private information. PMs spend resources on information Insiders often know things that are not public. IF even these guys cannot consistently generate risk-adjusted alpha, => markets ARE efficient in the strong form.

23. SO WHAT IS THE EVIDENCE FOR OR AGAINST THE EMH?
Insignificant runs and filter rule tests.
Insignificant daily return auto-correlation (serial correlation)
Later results positive over short horizons for portfolios (price momentum) but not for individual stocks;
Negative over long horizons (fads, overreaction).
Winner-loser returns and reversals (losers beat winners by a cumulative 25% over 3-years).
Other results on D/P, P/E, yield spreads appear to predict return
SO, SHORT RUN => MOMENTUM, LONG RUN => REVERSION

24. Evidence: semi-strong form (notion of event studies and abnormal returns)
Post-earnings announcement drift (sluggish, slow response)
January and tax-loss selling
Small firms (outperform 4.3% risk-adjusted)
Book-to-market (high performs better).
Neglected firms
Evidence: Strong form
Insider trades
Value line rankings
Fund manager performance

25. Alternative Exposition
No group of investors will consistently beat the market (T)
No investor will beat the market consistently over any time period (F)
Chances of finding an undervalued stock are 50/50 (T)
Minimizing trading activity provides superior returns to trading frequently (T)

26. Summary
The notion of efficient markets is one that is perhaps more pertinent for investors in developed capital markets. In that context, the key question to ask is: How efficient are markets? NOT Are markets efficient ?
Investors in markets that are developing are less concerned with this idea. However, the prevailing view is that the behavioral paradigm we referred to in past sessions does apply to both markets. Besides, there are several issues that merit consideration.
a) Magnitude issue ($ 5million gain on a $ 5 billion portfolio is still 1%)
b) Selection bias issue (the good strategies are never made public).
c) Lucky event issue (Warren Buffett, others like him??)