Risk and return of portfolio with probability

1. Return and risk of portfolio with probability
Shijin T P (12351047)
Suchil V (12351035)
Sankalp Sam Mathews (12351005)

2. contents
 INTRODUCTION
 THEORETICAL BACKGROUND
 ANALYSIS
 FINDINGS
 CONCLUSION

4. RESEARCH PROBLEM
 Always getting the probability estimated within the
Question??
 But how to arrive at the probability?

5. OBJECTIVE OF STUDY
 To understand the prediction of future security return
 To analyse the risk and return of individual securities
 To analyse the risk and return of portfolio

6. STUDY TOOLS
Regression
Ex ante return
Standard deviation
 Unsystematic risk
 Systematic risk (beta)
Portfolio return
Covariance
Portfolio risk

7. STUDY VARIABLES
 Closing price of various stocks from NSE
 Yahoo finance
 Closing value of Nifty

8. RESEARCH METHODOLOGY
 Secondary data :- stock prices from Yahoo finance and
NSE India.
 Predicting the future return and risk of share using
regression and fundamental analysis.
 Portfolio construction by considering the estimated
return and risk of securities.

9. The securities chosen
Industry
Company
Cement
ACC Ltd
Ultratech
Textile
Raymond
Grasim
Pharmaceutical
Ranbaxy
Dr. Reddy’s laboratories
Banking
Axis Bank
ICICI Bank
FMCG
Colgate Palmolive
Procter & Gamble

10. Limitations of the study
 Study based on past four years data
 The period was just after the financial crisis. So effects
of it was felt during this period. So data is slightly
biased negatively.
 Study based on 10 securities
 The 10 securities were taken randomly
 Probability assumption is subjective

11. •Investment is a sacrifice of current money or other resources for
future benefits.
•It is a planned decision to put money in financial assets with a riskreturn trade off.
•Numerous avenues of investment are available today.
Bank account
Long term government bond
Equity shares
Provident fund
Real estate
Other form
•Key aspects are time and risk

12. Why invest?
 Income
 Capital appreciation
 Tax advantages
 Hedge against inflation
 Preparation towards personal pension plan

13. Investment
Return
Risk

14. Return
 Return is the primary motivating force that drives
investment. It represents the reward for undertaking
investment.

Portfolio return is the expected return of the
security contained in the portfolio. It is determined on
the basis of proportion of the securities in portfolio.

15. Types of return
Ex Post Returns
 Return calculations done ‘after-the-fact,’ in order to
analyze what rate of return was earned.
Ex Ante Returns
 Return calculations may be done ‘before-the-fact,’ in
which case, assumptions must be made about the
future

16. Estimating Expected Returns
n
Expected Return (ER)
(ri
i 1
Where:
ER = the expected return on an investment
Ri = the estimated return in scenario i
Probi = the probability of state i occurring
Probi )

17. Portfolio return
 The Expected Return on a Portfolio is simply the
weighted average of the returns of the individual assets
that make up the portfolio.
n
E Rp
( wi
i
1
ER )
i

18. Risk
 Risk refers to the possibility that the actual outcome of
an investment will differ from its expected outcome
 Risk is defined as measurable possibility of loss on an
investment.

19. Types of risk
Systematic
risk
Interest
rate risk
Absolute risk
Unsystematic
risk
Purchasing
power risk
Business risk
Financial risk
Operational
risk

20. Measuring Risk
Ex ante Standard Deviation
n
Ex ante
(Probi ) (ri
ERi ) 2
i 1
Where:
ER = the expected return on an investment
Ri = the estimated return in state i
Probi = the probability of state i occurring

21. Portfolio Risk
2
p
= (wA)2
2
A
+ (wB)2
2
B
+ 2wAwB
Where,
wA =Weight of security A
wB = Weight of security B
2 =Variance of security A
A
2 = Variance of security B
B
A,B =Covariance between A and B
A,B

22. How to manage risk in
investment??

23. Risk and Return
Risk and return are the two most important
attributes of an investment.
Research has shown that the two are linked
in the capital markets and that
generally, higher returns can only be
achieved by taking on greater risk.
Risk isn’t just the potential loss of return, it
is the potential loss of the entire
investment itself (loss of both principal
and interest).
Retur
n%
Risk
Premium
R
F
Real Return
Expected Inflation Rate
Consequently, taking on additional risk in
search of higher returns is a decision that
should not be taking lightly.
Ris
k

24. Probability
 Probability is a measure or estimation of likelihood of
occurrence of an event. Probabilities are given a value
between 0 and 1.
 The higher the degree of probability, the more likely the
event is to happen, or, in a longer series of samples, the
greater the number of times such event is expected to
happen.
Investment decisions are based on future events .
Future is uncertain . To deal with uncertainty
probability is used .

26. Contents
 Predicting various possible states of economy most
likely to occur and their probability of it occurring.
 Estimating return and risk of individual securities
 Construction of portfolio using Sharpe’s model
 Estimating return and risk of portfolios

27. Positives for the economy
Negatives for the economy

28. Positive signs from the Indian
Economy
 Good monsoon so good agricultural output likely
 High investment in infrastructure likely.
 Effects of recession slowly receding.
 Exports rising.

29. Negative signs from the Indian
economy
 GDP growth down from 8.3% in 2008-09 to 3.99% in
2012-13
 Current Account Deficit gone up from $8bn in 2007 to
$ 90 bn
 But foreign exchange reserves comes down from $300
bn to $275 bn. It can cover now only 3 times the CAD
against the 37.5 times in 2007.
 Inflation at alarming rates.

30. Negative signs(contd)
 Rupee depreciation and volatility
 Fast reemerging US economy. Interest rates going up
and so attracts investors to US. DOUBLE BLOW TO
INDIAN RUPEE.
 $170 billion in short term debt to pay.
 Political confusion

31. What rating agencies says?
 S&P: BBB- “negative outlook”
 Moody’s: “stable”.
Above 6% growth predicted next year.
 Fitch: “stable”.
5% growth predicted next year.

32. Growth predictions
 IMF:
3.8% in this year. 5.1% in 2014.
 World Bank expects India to grow by 4.7% this fiscal.
 Moody’s: Above 6% in 2014
 Fitch: 5% in next fiscal.

33. Various states of economy
State
Definition
Probability
1
Effects of recession continues
35%
2
Economy limping to normalcy
35%
3
Economy getting worse
20%
4
High growth
5%
5
Economy getting into recession
5%

34. Prediction of future price
 We use regression of past 4 years to predict the future
price of 1 year.
 The predicted values using regression are:Company
Return
ACC
32.34%
Ultratech
23.06%
Raymond
55.53%
Grasim
17.69%
Axis Bank
12.98%
ICICI
13.61%
P&G
11.73%
Colgate Palmolive
28.88%
Dr. Reddy's lab
-1.37%
Ranbaxy
14.54%

35. Prediction of future price(contd)
 Based upon the regression derived value, we derive one
year return.
 Based upon the regression derived return (arrived
above), we make changes based on the industry
analysis as shown in following slides.

36. Cement Industry
 India to invest heavily in infrastructure.
 Good news for cement industry.
 5% Upward estimate

37. Textile Industry
 Indian Textile Ministry estimates the size of textile
output in the country to expand.
 CAB forecasts record output of cotton despite area
under cultivation coming down.
 Positive output.
 5% upward estimate.

38. FMCG Industry
 Good and even monsoon.
 Good agricultural output means more money with
rural folk.
 Positive impact
 7% Upward estimate

39. Banking Industry
 12 new foreign banks to enter India.
 RBI to come out with measures to encourage foreign
banks to convert into wholly owned subsidiaries
(WOS) that provides near national treatment. It
intends to provide level playing field with domestic
banks.
 A blow to domestic banks.
 Negative outlook to them.
 Downward estimate by 10%.

40. Pharmaceutical companies
 Dr. Reddy’s Laboratories
 Sales in India, Russia and CIS nations increased by
42%.
 Revenues rose up by 16.5%.
 An upward estimate of 5%.

41. Pharmaceutical companies(contd)
 Ranbaxy:
 In May 2013 the US fined the company US$500 million
after it was found guilty of misrepresenting clinical generic
drug data and selling adulterated drugs to the United
States.
 Sep 2013: Human hair and unhygienic preparations.
Banned from using Mohali facility.
 Poor oversight and inadequate testing and maintenance of
drugs manufactured at its facilities in Paonta Sahib and
Dewas, India. Compensation paid is $350million.
 Downward estimate of 10%.

42. The new returns are:-(note that this is also the return for the 1st
state of economy i.e., if effects of recession continues(but after
considering industrial analysis)
Company
Revised Return
ACC
33.96%
Ultratech
24.21%
Raymond
58.30%
Grasim
18.57%
Axis Bank
11.68%
ICICI
12.25%
P&G
12.55%
Colgate Palmolive
30.90%
Dr. Reddy's lab
-1.30%
Ranbaxy
13.09%

43. For other states of economy, returns near to it (either decrease or
increase based on the state of economy is given). An example for
ACC is given here.
ACC
State
Probability
32.34%
1
35%
33.96%
2
35%
35.65%
3
20%
25.47%
4
5%
42.45%
5
5%
22.07%

44. n
Expecte Return (ER)
d
( ri Probi )
i 1
Where:
ER = the expected return on an investment
Ri = the estimated return in scenario i
Probi = the probability of state i occurring
calculation

45. Expected risk
n
Ex ante
(Probi ) (ri
ERi ) 2
i 1
Where:
ER = the expected return on an investment
Ri = the estimated return in state i
Probi = the probability of state i occurring

46. The calculation for ACC is given
here..
ACC
Probability
state
Expected Return
Return
Expected Return
Ri-E( R )
Standard
Deviation
Variance
1
0.35
33.96%
11.88%
1.27%
0.0000568
2
0.35
35.65%
12.48%
2.97%
0.0003090
3
0.2
25.47%
5.09%
-7.22%
0.0010414
4
0.05
42.45%
2.12%
9.76%
0.0004765
5
0.05
22.07%
1.10%
-10.61%
0.0005630
32.68%
0.0024466
4.95%

47. Sharpe model
 Step1 :calculate excess return to beta ratio of each security.
 Step 2:Review and rank the excess return to beta ratio in the
order from higher to lowest.
 Step 3:Rearrange the data with securities in order to rank
determine in step 2
 Step 4:determine the cut off point by applying the following
formula for each security.

48.  Step 5 :select the securities to be included in the
portfolio by comparing excess return to beta ratio and
determine cut off point for each security
If excess return to beta ratio is greater than
cut-off rate calculated all such securities should be
included
 Step 6:Determine over all cut-off rate (c*)by selecting
the cut-off point of last securities among them
securities which are included in the portfolio

49.  Step 7:Determine the weight or proportion of funds
to be invested in each selected securities of the
optimum portfolio by applying the following formula
Where,
calculation

50. The weights calculated are:Company
Weight
Raymond
37.66%
Axis Bank
62.34%

51. Expected return of portfolio
n
ERp
( wi ERi )
i 1
Portfolio return

52. Expected risk of portfolio
2
p
= (wA)2
A,B
=
2
A
+ (wB)2
2
B
+ 2wAwB
A,B
pi(RAi - E[RA])(RBi - E[RB])

53. Findings
Raymond
Axis Bank
ACC
ICICI
Colgate Palmolive
Grasim
Ultratech
P&G
Dr. Reddy's lab
Ranbaxy
Risk
Expected Return
56.12%
11.25%
32.68%
11.79%
29.74%
17.88%
23.30%
12.08%
-1.35%
12.60%
8.49%
1.70%
4.95%
1.78%
4.50%
2.71%
3.53%
1.83%
0.19%
1.91%

54. Findings(continued)
Securities
Raymond
Axis Bank
Weight
37.66%
62.34%

55. Findings(continued)
Portfolio Return
Portfolio Risk
28.14%
4.26%

56. Conclusion
 Past data as well as fundamental analysis helps us in
predicting the future value of a security, thus enabling
us to predict the return available with the security.
 It also helps us in constructing a portfolio wherein our
predicted values may be used to calculate the portfolio
risk and return.