Test Validity of VaR analysis of Mutual Funds

The construct of Value at-risk ( VaR ) as a individual hazard step sum uping all beginnings of Downward hazard, has gained popularity in recent old ages, among bankers, portfolio directors and finance fraternity in general. The current survey efforts to foreground the importance of VaR as a step of ‘downside hazard ‘ for Indian common financess, an facet which is wholly ignored for public presentation coverage in Indian common fund industry. The survey used three parametric theoretical accounts and one non parametric theoretical account and hebdomadal returns of a sample of equity common fund strategies in India, to foretell their hebdomadal VaR on a ‘rolling ‘ footing and besides tested the hardiness and prognostic ability of the theoretical accounts by using two popular ‘back proving ‘ attacks. Overall the analysis shows that the Indian common financess have exhibited considerable downside hazard in footings of VaR steps. Back testing of the theoretical accounts suggest that the ‘random walk ‘ and the ‘moving norm ‘ theoretical accounts suffer from a downward prejudice and err by undervaluing the VaR often. The EWMA and historical simulation theoretical accounts are free from that prejudice, but these two theoretical accounts, peculiarly the later, show inclination of supplying excessively conservative estimations of VaR.

Introduction

Common Fund Industry

Common Fund is a trust that pools the nest eggs of a figure of investors who portion a common fiscal end. The money therefore collected is so invested in capital market instruments such as portions, unsecured bonds and other securities. The income earned through these investings and the capital grasp realized is shared by its unit holders in proportion to the figure of units owned by them. Thus a Common Fund is the most suited investing for the common adult male as it offers an chance to put in a diversified, professionally managed basket of securities at a comparatively low cost.

The flow chart below describes loosely the working of a common fund:

Types of Mutual Fund Schemes

Wide assortment of Mutual Fund Schemes exists to provide to the demands such as fiscal place, hazard tolerance and return outlooks etc.

The tabular array below gives an overview into the bing types of strategies in the Industry.

VaR ( Value-at-Risk )

The construct of Value at Risk ( VaR ) as a individual hazard step sum uping all beginnings of downside hazard was foremost developed by J. P. Morgan and made available through its Risk-Metrics package in October 1994.

Value-At-Risk ( VaR ) answers the inquiry, “ How much can the value of a portfolio diminution with a given chance in a given clip period? ”

The most common premise is that returns follow a normal distribution. One of the belongingss of the normal distribution is that 95 per centum of all observations occur within 1.96 standard divergences from the mean. This means that the chance that an observation will fall 1.96 standard divergences below the mean is merely 2.5 per centum. For the intents of ciphering VAR we are interested merely in losingss, non additions, so this is the relevant chance.

Example: A XYZ Fund hasA an ( arithmetic ) mean monthly return of 2.03 per centum and a standard divergence of 3.27 per centum. Therefore, its monthly VAR at the 2.5 per centum chance degree is 2.03 % -1.96*3.27=-4.38 % , or $ 43.80 for a $ 1,000 investing, intending that the chance of losing more than this is 2.5 per centum.

LITERATURE REVIEW

Some of the practical and computational issues related to utilizing VaR are discussed in Soumya Guha Deb Ashok Banerjee ( 2009 ) .The rebalancing of VaR is discussed by T.B.Kapali, besides Darryll Hendricks has comprehensively explained Evaluation of VaR Models Using Historical Data. Finally a paper by Charles Cao and Eric Chang as been referred to which Studies of dynamic relationship between common fund flow and market volatility. Joseph Messina ( 2003 ) noted that VaR is concerned chiefly with ruinous events and so its ability to adequately stand for hazard penchants of investors is badly limited.

VaR is defined as the expected maximal loss ( or worst loss ) over a mark clip skyline within a given assurance interval. VaR therefore has two parameters-the clip skyline over which the alteration in the portfolio value is being monitored and the assurance degree at which the estimation is being made. To give an illustration, if a portfolio has a day-to-day VaR of Rs. 1 million with 95 % assurance degree, it means that over the following 20 four hr period, there is merely 5 % opportunity the portfolio value will cut down by an sum more than Rs. 1 million. Alternatively stated, the likeliness of sing a one-day loss less than Rs. 1 million is 95 % . This individual figure summarizes the fund director ‘s exposure to downside market hazard from all beginnings, every bit good as to the chance of an inauspicious motion.

The current survey efforts to foreground the importance of VaR as a step of ‘downside hazard ‘ for Indian equity common financess, an facet which is wholly ignored for public presentation coverage in Indian common fund industry. Common Funds in India still utilize standard divergence as the exclusive step to describe hazard of financess. The current survey used three parametric theoretical accounts ( viz. random walk theoretical account, traveling mean theoretical account, and the exponentially leaden traveling mean theoretical account ) and one non parametric theoretical account ( historical simulation ) and a ‘rolling window ‘ of past hebdomadal returns of a sample of equity common fund strategies in India, to gauge the volatility of the series and use that estimation to foretell the hebdomadal VaR of each of the strategies. The survey compared the existent alterations in NAV or existent return generated by the strategies to happen out whether the existent downsides exceed the predicted VaR s by the theoretical account station facto. This would give us an thought of the degree of downside hazard of equity common financess in India. The survey besides tested the prognostic ability of the different theoretical accounts used utilizing a model proposed by Jorion ( 2001 ) and Kupiec ( 1995 ) depending on the figure of instances where the existent downside encountered by the financess exceeded the VaR predicted by the theoretical accounts.

Working with a sample of 60 Indian equity common fund schemes our analysis shows that the hebdomadal return matching to 99 % VaR for equity common financess range from -5.4 % to -12.4 % about and that matching to 95 % VaR ranges from -3.9 % to – 5.8 % about for the assorted theoretical accounts used. The statistical trials of the theoretical accounts based on a model mentioned above suggest that the random walk theoretical account and the moving mean theoretical accounts suffer organize a downward prejudice and err by undervaluing the VaR. The EWMA and historical simulation methods are free from that prejudice but they show a few cases of supplying excessively conservative estimations of VaR.

Validity Test

Aim

To formalize usage of VaR as a Risk Measure of Common Fundss in India

Datas

The survey used the hebdomadal NAV of ‘mutual financess ‘ for our analysis. These hebdomadal NAVs were taken from Bloomberg. We used these hebdomadal NAV values to cipher the continuously compounded hebdomadal return figures of the financess for our analysis as follows:

Methodology

The survey used three widely used parametric theoretical accounts and one non parametric theoretical account to gauge the hebdomadal volatility of the return series and that estimation is in bend employed to gauge the VaRs for the equity common financess in our sample. The survey besides test the hardiness of the theoretical accounts by using two back proving methodological analysiss.

The theoretical accounts and attacks employed by the survey are discussed hereunder:

Parametric Approach/ Analytical VaR

Three parametric theoretical accounts are used to acquire the estimation of volatility for doing VaR anticipations. They are as follows:

Random walk theoretical account ( RW henceforth )

The random walk theoretical account is the simplest of the theoretical accounts considered which makes a naA?ve premise that tomorrow ‘s volatility depends on today ‘s volatility. Based on the premise that the expected return over a long adequate clip series being zero, the theoretical account is more simplistically given by:

Traveling Average theoretical account ( MA henceforth )

This is an extension of the random walk theoretical account. The survey used a four hebdomad traveling mean theoretical account given by:

Exponentially Weighted Moving Average theoretical account ( EWMA henceforth )

Exponentially Weighted Moving Average theoretical account, where the weights assigned to past informations lessening exponentially as we move back through clip. The theoretical account is given by the look as follows:

The estimation I?t of the volatility for period ‘t ‘ ( made at the terminal of period ‘t-1 ‘ ) is calculated from I?t-1 ( the estimation that was made at the terminal of period ‘t-2 ‘ of the volatility for period ‘t-1 ‘ ) and r t-1 ( the most recent period return of the security ) .

Non-Parametric Approach: Historical simulation method

Historical simulation is one of the popular ways of gauging VaR. This attack involves use of past informations in a really direct manner as a usher to what might go on in the hereafter. The historical simulation technique and the parametric methods described above are similar to the extent that they all rely to a certain extent on past observations. But alternatively of utilizing these past observations to cipher the portfolio ‘s standard divergence ( the underlying premise being that the future distribution of the security ‘s value alteration follow a normal distribution ) , the historical simulation attack assumes that, the distribution of historical returns of a security is itself an estimation of the future distribution of value alterations of the security. Once the hereafter distribution is known, the historical simulation technique uses existent percentiles of the observation period as VaR steps. For illustration for an observation series of 100 hebdomads, the 95 % assurance degree VaR is the 5 percentile value in the series. Similarly for 99 % assurance degree, the VaR estimation will be the 1 percentile value in the series. It is assumed in this attack that the correlativities and volatilities that are calculated in the parametric attack are all embedded in the monetary value informations that the historical technique utilizations.

Given about 364 hebdomadal return figures we used past 200 hebdomadal figures at a clip to represent the future return distribution for the 201st hebdomad and used that to acquire the VaR estimation at 95 % and 99 % assurance degrees, by the process described as above. These estimated Volt-ampere at both degrees of assurance are so compared station -facto with the existent alteration in NAV and the entire figure of ‘exceptions ‘ noted as for the parametric attack. The procedure is repeated for each fund individually.

Back testing of the theoretical accounts:

“ Back proving ” of the theoretical accounts described above involves consistently comparing estimated VaR measures with existent fluctuations in the security ( or portfolio ) value station facto. Now since VaR is reported merely at a specified assurance degree, we expect the figure to be exceeded in some cases, for illustration, in 5 % of the observations at the 95 % assurance degree. But it may non go on that we observe precisely 5 % extra divergences. A greater per centum could happen due to bad fortune or opportunity.

However, if the frequence of divergences becomes excessively big, say, 10 to 20 per centum, the user must reason that the job lies with the theoretical account, non bad fortune or opportunity and undertake disciplinary action. The of import issue is how to do this determination and involves a classical statistical determination job.

RESULTS & A ; ANALYSIS

Table 1 below shows the list of financess in the survey sample along with fluctuations in their NAVs during the survey period. One can clearly see the considerable downside swings exhibited by the financess from the magnitude of the ‘downside SD ‘ which ranges from 10 % to 30 % of the average NAV. Given that these are base on hebdomadal NAV informations, such magnitude of downside swings calls for a farther geographic expedition of downside hazard degrees of the financess.

Table1: List of financess in the survey sample demoing fluctuations in their NAV during the survey period

Sr. No

Fund Name

Option

Get downing NAV

Peak NAV

Min NAV

Mean NAV

Downside

South dakota

Downside

SD as a %

of Mean

NAV

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

B O B Equity Linked Salvaging

Birla Tax Plan ’98

Franklin India Taxshield 97

Franklin India Taxshield 99

Sundaram Tax Saver

B O B Equity Linked Saving Scheme-1996

Birla Equity Plan

Canequity Tax Saver

Franklin India Taxshield

Licmf Tax Plan

Principal Personal Tax Saver

Chief Tax Savings Fund

S B I Magnum Tax Addition

Sahara Tax Gain Fund

Tata Tax Saving Fund ( Open )

Birla Advantage Fund

Birla India Opportunities Fund

Birla India Opportunities Fund

Birla M N C Fund

Birla M N C Fund

Canexpo

Chola Opportunities Fund

Chola Opportunities Fund

D S P Merrill Lynch Equity Fund

Franklin Fmcg Fund

Franklin India Bluechip Fund

Franklin India Bluechip Fund

Franklin India Prima Fund

Franklin India Prima Fund

Franklin India Prima Plus

Franklin India Prima Plus

Franklin Infotech Fund

Franklin Infotech Fund

Franklin Pharma Fund

I N G Vysya Select Stocks Fund

J M Basic Fund

Jm Equity Fund

Jm Equity Fund

Kotak Mahindra 30 Unit Scheme

Licmf Equity Fund

Prudential Icici Fmcg Fund

Prudential Icici Growth Plan

Prudential Icici Growth Plan

Prudential Icici Power

Reliance Growth Fund

Reliance Growth Fund

Reliance Vision Fund

S B I Magnum Contra Fund

S B I Magnum Equity Fund

S B I Magnum F M C G Fund

S B I Magnum I T Fund

S B I Magnum Multiplier Plus-1993 ( Open )

S B I Magnum Pharma Fund

Sundaram Growth Fund

Tata Growth Fund

Tata Life Sciences & A ; Technology Fund

Tata Pure Equity Fund

Tata Select Equity Fund

Taurus Discovery Stock Fund

Templeton India Growth Fund

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Dividend

Growth

Dividend

Growth

Growth

Growth

Dividend-Q

Growth

Growth

Dividend

Growth

Growth

Dividend

Dividend

Growth

Growth

Dividend

Growth

Growth

Growth

Dividend

Growth

Growth

Growth

Growth

Dividend

Growth

Growth

Dividend

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

Growth

14.95

47.29

43.27

30.45

11.42

19.06

26.88

26.15

23.40

17.30

46.35

24.20

42.06

81.72

43.23

62.83

24.98

24.98

38.89

38.89

23.43

16.92

13.91

27.71

14.98

45.59

51.35

34.58

30.82

27.00

30.24

69.89

63.04

13.89

20.41

22.69

16.68

15.71

23.32

11.23

12.93

26.26

30.26

18.61

42.63

42.63

26.20

13.93

33.75

13.83

34.38

32.76

14.12

21.18

5.38

18.44

14.96

23.59

6.37

15.09

49.24

202.94

121.26

74.10

19.63

32.47

56.16

33.14

128.68

27.38

143.41

80.71

63.07

121.70

56.97

125.58

35.51

52.20

62.14

123.94

55.54

27.92

18.15

46.02

39.11

53.92

131.67

214.36

67.00

38.53

137.53

70.95

64.00

30.97

36.58

26.74

20.15

39.25

68.34

21.27

41.29

34.17

93.99

77.31

57.20

266.74

183.67

37.96

55.44

22.05

52.97

53.04

41.24

68.63

31.84

48.61

61.84

48.55

16.41

65.39

7.39

19.39

18.70

11.18

6.19

7.58

9.54

7.48

16.33

5.61

32.64

9.19

9.56

13.63

8.48

19.63

5.32

5.83

20.85

23.18

8.54

6.93

4.40

10.23

9.58

8.22

14.88

13.94

8.74

9.65

15.34

7.47

5.11

7.94

4.52

6.84

6.17

5.59

9.27

4.43

7.25

7.41

14.12

9.70

11.95

16.13

11.91

6.37

6.69

5.24

4.38

6.89

7.99

8.70

5.23

7.73

7.74

5.97

3.13

9.30

18.72

72.80

49.77

30.47

12.03

17.07

24.75

14.89

50.06

13.57

72.39

28.94

27.34

44.39

22.44

51.24

14.42

22.21

34.26

52.12

23.71

13.41

8.76

22.50

17.05

20.89

48.29

73.69

28.74

20.36

47.82

24.37

14.95

15.11

13.21

14.58

11.78

15.13

25.69

10.39

15.70

13.76

36.23

24.47

29.96

81.69

59.11

14.53

15.07

10.16

11.70

19.98

16.29

25.68

12.54

18.32

22.73

17.66

7.55

26.18

3.18

15.51

8.31

5.05

1.26

2.26

4.33

1.96

7.48

2.60

7.68

5.62

5.38

9.45

3.31

9.28

2.32

4.49

3.59

7.52

4.44

1.65

1.17

3.19

1.84

3.38

7.58

15.22

4.94

2.83

7.35

3.77

2.13

1.61

2.06

1.89

1.58

2.68

4.84

1.50

1.75

1.65

5.77

3.81

4.49

19.11

11.64

2.00

2.43

1.44

2.00

3.75

1.87

4.60

1.80

3.17

4.12

3.48

1.36

3.63

17 %

21 %

17 %

17 %

10 %

13 %

17 %

13 %

15 %

19 %

11 %

19 %

20 %

21 %

15 %

18 %

16 %

20 %

10 %

14 %

19 %

12 %

13 %

14 %

11 %

16 %

16 %

21 %

17 %

14 %

15 %

15 %

14 %

11 %

16 %

13 %

13 %

18 %

19 %

14 %

11 %

12 %

16 %

16 %

15 %

23 %

20 %

14 %

16 %

14 %

17 %

19 %

11 %

18 %

14 %

17 %

18 %

20 %

18 %

14 %

The fundwise mean of estimated hebdomadal VaRs of the financess ( from 201 hebdomad to 364 hebdomad. ) is shown in tabular arraies 2 below. The typical hebdomadal VaR estimations have ranged from -3 % for some financess to every bit high as -22 % for some financess for assorted degrees of assurance. Now these estimations are based on hebdomadal NAV information.

Table 2: Fundwise modelwise average hebdomadal VaR estimations during the 201 to the 364 hebdomad

These hebdomadal estimations translate into typical one-year VaRs in the scope of about 40 % to 90 % at 99 % degree of assurance and about 28 % to 44 % at 95 % degree of assurance. It may therefore be commented that the downside hazard of the equity common financess in India are rather significant. It may be seen that the VaR estimations obtained by utilizing the historical simulation attack ( peculiarly ) at 99 % degree are far higher than the estimations obtained by other theoretical accounts. But the difference reduces to a great extent at 95 % degree. This should connote that a few utmost market motions have well affected our estimations by the historical simulation attack given that the historical simulation attack employs full past information set itself as an estimation of future distribution.

Table 3 below shows the fundwise and modelwise figure of ‘exceptions ‘ observed in the existent NAV motions vis-a-vis the predicted VaRs. The figure of VaR estimations being 164 ( 201 hebdomad to 364 hebdomad ) the Numberss given in the tabular array indicate the Numberss of instances out of these 164 instances where the existent alteration in NAV ( downside motion ) has exceeded the predicted VaR.

Table 3: Fundwsie modelwise no. of ‘exceptions ‘ observed out of 164 VaR projections made based on a turn overing 200 hebdomad past informations. Numbers within parenthesis indicate the figure of exclusions for the 95 % VaR and the figure outside the parenthesis indicate the figure of exclusions over the 99 % VaR

The sum-up of the consequences of ‘back testing of the theoretical accounts ‘ based on the ‘failure rate attack ‘ and the ‘log-likelihood ratio ‘ attack is shown in table 4 below. The entire figure of predicted VaRs being 164, the figure of exclusions or failures ( instances when the existent downside alteration in NAV for the fund exceeded that predicted by VaR estimations ) expected for the 99 % VaR estimation should be around 1.64 or about 2, while that for the 95 % VaR should be around be around 8.2 i.e between 8 to 9. However as we can see from the tabular array 3 above, for the random walk theoretical account every bit good as for the four hebdomad traveling mean theoretical account, for all the financess, the figure of exclusions observed are far higher. This is farther confirmed by the figure of important and positive Z-stat figures obtained for these theoretical accounts

for both 99 % and 95 % VaRs. It can therefore safely be concluded that these two theoretical accounts underestimate the VaR for the financess to a big extent and should be unsuitable for usage to foretell the VaR of equity financess in India. For the EWMA and historical simulation theoretical accounts nevertheless, the figure of exclusions or failures are merely about within the expected scope and hence the figure of positive and important Z-sat values or Chi square values are hence comparatively less. However it may besides be noted that in the ulterior theoretical accounts there are a few occasions when the figure of exclusions really observed are far less than that expected taking to coevals of negative and important Z-stat figures. Therefore there is a possibility that these theoretical accounts are bring forthing excessively conservative estimations of VaR at times.

Table 4: Statistical Test consequences of back proving with the figure of exclusions observed

The Numberss in the cells indicate the figure of financess out of a sample of 60 for which the Z-stat or Chi square has come out to be significantly positive or negative

On the whole our analysis shows that equity common financess have a considerable downside hazard measured in footings of VaR, to the melody of 40 % to 90 % at 99 % degree of assurance and about 28 % to 44 % at 95 % degree of assurance. Out of the four chief theoretical accounts that we have used, the random walk and the four-week moving norm theoretical accounts are biased downwards and err by undervaluing the VaR on a regular footing, while the EWMA and historical simulation theoretical accounts are comparatively free signifier that prejudice. They nevertheless show a few cases of supplying excessively conservative VaR estimations but one possibly has to populate with that to avoid a downside calamity. The historical simulation method may be modified by disregarding the outliers in the past return series, depending on the research worker ‘s position about the possibility of the utmost events that caused such outliers, to reiterate, during her clip skyline of gauging VaR.

Decision

Traditionally, hazard of portfolios has been measured utilizing historical returns and the correlativities between the assets consisting it. These hazard steps have the serious shortcoming that they are all rearward looking. In contrast VaR provides a forward looking, individual, comprehensive step sum uping assorted beginnings and quantum of hazard for portfolios. This belongings has been punctually recognized by the banking industry and VaR has rapidly found credence over at that place but practicians in the investing industry are a small disbelieving to follow VaR as a step of hazard chiefly because of the cardinal differences in the relevant clip skylines of the two industries. However as has been argued in some recent surveies, investing establishments besides greatly benefit from the subject provided by hazard direction systems integrating VaR based model.