Optimal Portfolio: drawn from empirical studies

In this exposition we will consider an optimal portfolio consisting of Mutual Funds. To accomplish this we must select a benchmark index then relate each fund to this benchmark. The next computation will be systematic and unsystematic risk. Then we must compute the Cut Off Point which will enable the calculation of the optimum portfolio.

First we calculate a risk free rate of return. A proxy for Risk Free Rate can be Government Bonds. The calculation for Risk Free rate is set out below.
Year Opening Index Closing Index Ri (cls-open)/op*100
2007-2008 4865.90 5177.60 6.40
2008-2009 5295.01 5420.2 2.36
2009-2010 5846.48 6368.53 8.92
2010-2011 6399.96 7206.86 12.60
2011-2012 7282.15 6570.18 -9.77

 

 

 

Year RM (Rm-R!m) (Rm-R!m)^2
2007-2008 6.40 2.3 5.29
2008-2009 2.36 -1.74 3.02
2009-2010 8.92 4.82 23.23
2010-2011 12.60 8.5 72.75
2011-2012 -9.77 -13.87 192.37
Totals 20.51   296.16

From tables above calculate the Variance of the Market Index

R?m = SRm÷N = 20.51/5 = 4.10

sm2 = S (Rm-R?m) 2/N-1 = 296.16/ 4 = 74.04

Risk and Return Calculation on Selected Funds (Net Asset Value (NAV) ,fund return and variance.

Year NAV Beginning NAV End Ri (End-Beg)/beg*100
2007-8 70.10 76.10 8.56
2008-9 76.98 88.39 14.82
2009-10 89.15 98.14 10.08
2010-11 99.95 116.84 16.89
2011-12 117.12 127.94 9.23

 

 

Years Ri (Ri-?R?i) (Ri-?R?i)^2 (Rm-Rm?) (Rm-Rm?)^2 (Ri-?R?i) (Rm-Rm?)
2007-8 8.56 -3.35 11.22 2.3 5.29 -7.7
2008-9 14.82 2.91 8.46 -1.74 3.02 -5.06
2009-10 10.08 -1.83 3.34 4.82 23.23 -8.82
2010-11 16.89 4.98 24.8 8.5 72.25 42.33
2011-12 9.23 -2.68 7.18 -13.87 192.37 37.17
Totals 59.58   55   296.16 57.92

Calculation of variance of Birla sun life

R?i = SRi/N

= 59.58/5

= 11.91

si2 = S (Ri-R?i) 2/N-1

= 55/4

= 13.75

Systematic Risk: ßi = S (Ri-R?i) (Rm-R?m)/ (Rm-R?m) 2

= 57.92/296.16

= 0.1955

Unsystematic Risk: se?i2 = si2-ßi2sm2

= 13.75 - (0.19552*74.04)

= 13.75 -2.829

= 10.92

SBI Magnum Midcap Fund

Year NAV Beginning NAV Ending Ri (end-beg)/beg*100
  74.82 68.48 -8.47
  69.87 79.77 14.16
  80.05 94.35 17.86
  94.91 104.01 9.58
  103.74 97.64 -5.88

Table 6: NAV and fund return of SBI Magnum Midcap Fund.

Years Ri (Ri-?R?i) (Ri-?R?i)^2 (Rm-Rm?) (Rm-Rm?)^2 (Ri-?R?i) (Rm-Rm?)  
2007-8 -8.47 -13.92 193.76 2.3 5.29 -32.01  
2008-9 14.16 8.71 75.86 -1.74 3.02 -15.15  
2009-10 17.86 12.41 154.008 4.82 23.23 59.81  
2010-11 9.58 4.13 17.05 8.5 72.25 35.1  
2011-12 -5.88 -11.33 128.36 -13.87 192.37 157.14  
Totals 27.25   569.03   296.16 204.89  

Table 7: Calculation of variance of SBI Magnum Midcap Fund

R?i = SRi/N

= 27.25/5

= 5.45

si2 = (Ri-?R?i) 2/n-1

= 569.03/4

= 142.25

Systematic Risk: ßi = S (Ri-?R?i) (Rm-Rm?)/(Rm-Rm?) 2

= 204.89/296.16

= 0.6918

Unsystematic Risk: se?i2 = si2-ßi2sm2

=142.25 - (0.69182*74.04)

= 142.25 – 35.4345

= 106.81

Kotak Classic Equity Fund

The below given Tables 8 and 9 shows the NAV and fund return and Calculation of Kotak Classic Equity Fund. R?i = SRi/N

Year NAV Beginning NAV End

Ri (end-beg)/beg*100
2007-8 62.30 66.30 6.42
2008-9 66.95 72.58 6.40
2009-10 73.07 83.41 14.15
2010-11 142.10 141.20 -0.63
2011-12 141.88 141.73 -0.10

Table 8: NAV and fund return of Kotak Classic Equity Fund.

Years Ri (Ri-?R?i) (Ri-?R?i)^2 (Rm-Rm?) (Rm-Rm?)^2 ?(Ri-?R?i) (Rm-Rm?)
2007-8 6.42 0.78 0.608 2.3 5.29 1.79
2008-9 8.40 2.75 7.61 -1.74 3.02 -4.80
2009-10 14.15 8.51 72.42 4.82 23.23 41.01
2010-11 -0.63 -6.27 39.31 8.50 72.25 -53.29
2011-12 -0.10 -5.74 32.94 -13.87 192.37 79.61
Totals 28.24   152.88   296.16 64.32

Table 9: Calculation of variance of Kotak Classic Equity Fund.

R?i = SRi/N

= 28.24/5

= 5.64

si2 = S (Ri-R?i) 2/n-1

= 152.88/4

= 38.22

Systematic Risk: ßi = S (Ri-R?i) (Rm-R?m)/(Rm-R?m) 2

= 64.32 /296.16 = 0.2171

Unsystematic Risk: se?i2 = si2-ßi2sm2

= 38.22 - (0.21712*74.04)

= 38.22 –3.4896

= 34.73

Due to demand the above exposition is published prior to full completion. The complete exposition will be added shortly.