Investment Planning: Asset Relocation 6 (Checking the New Component in Strengthen the Sharpe Optimization via Excel Solver)

Lately, I discovered a good unit trust from an article that presented its ten years performance since 3-Jul-00 to 19-Aug-10. It is surprisingly its annualized return and standard deviation is much more better than my own portfolio. Let us name this unit trust as PSC.
Annualized Return = RATE((DATE(2010,8,19)-DATE(2000,7,3))/365.25,0,-1,4.0809) = 14.90% p.a.
So, I am introducing this unit trust to my current portfolio for the optimization.

Result:
A) Single Unit Trust
Expected Return: 2.95%, Standard Deviation: 3.21%, Sharpe Ratio: 0.8540
B) Current Optimized Portfolio
Expected Return: 3.30%, Standard Deviation: 2.35%, Sharpe Ratio: 1.3136
C) Introducing PSC into Current Optimized Portfolio
Expected Return: 3.34%, Standard Deviation: 2.16%, Sharpe Ratio: 1.4524
D) Actual Portfolio
Expected Return: 3.11%, Standard Deviation: 3.58%, Sharpe Ratio: 0.8097

Action 1:
What Happen if I relocate Genting to LPI and PIttikal to PSC?
Expected Return: 3.35%, Standard Deviation: 3.38%, Sharpe Ratio: 0.9304


Action 2:
What Happen if I relocate PIttikal to PSC?
Expected Return: 3.25%, Standard Deviation: 3.49%, Sharpe Ratio: 0.8695

Action 3:
What Happen if I relocate Genting and PIttikal to PSC?
Expected Return: 3.26%, Standard Deviation: 3.35%, Sharpe Ratio: 0.9095

Investment Planning: Asset Relocation 5 (Sharpe Optimization via Excel Solver)

This is the June-2010 Sharpe optimization.

Current Portfolio: Return = 3.28%, STDEV = 4.21%, Sharpe = 0.7471
Optimized Portfolio: Return = 3.44%, STDEV = 2.68%, Sharpe = 1.210
Solver improvement: Significant improvement on the STDEV results better sharpe ratio

Scenario 1: What happen if I invest EPF RM13,000 into PRSF?
Return = 3.22%, STDEV = 3.98%, Sharpe = 0.7573
No significant improvement on sharpe. However, EPF money is limited to invest in selected fund e.g. PRSF.

Scenario 2: What happen if I invest Cash RM13,000 into LPI?
Return = 3.30%, STDEV = 3.97%, Sharpe = 0.7773
No significant improvement on sharpe.

Scenario 3: What happen if I relocate RM13,000 from Genting to LPI?
Return = 3.38%, STDEV = 3.98%, Sharpe = 0.7960
No significant improvement on sharpe.

Scenario 4: what if I follow as per optimized?
Return = 3.44%, STDEV = 2.68%, Sharpe = 1.210
Significant improvement on sharpe. The result gives me a shock. 5-component-portfolio gives a better sharpe ratio than 13-component-portfolio. I might make a lot of mistakes that believe on investing more stocks will dilute the risk as the number of stock increases. My possible mistake in the past may be adding too many components that not really "diluting" the risk.

As I learn from here, risk-return research must be studied after the stock picking from fundamental selection. It is because you never know the characteristic of your good fundamental stock in helping the risk dilution or risk concentration.

Investment Planning: Asset Relocation 2

Let us take the 5 stocks as example for two methods of asset relocation.

First method:
The first method was shown in the previous blog titled "Investment Planning: Asset Relocation".
Scenario:
10-month-performances for five stocks were tabulated as a study case.
Stock i average return = AVERAGE(array stock i)
Stock i standard deviation = STDEV(array stock i)

Risk free rate = 2.5%/12 = 0.21% per month

Desired return = 2.5% per month

Sharpe Ratio = (Average Return - Risk Free)/Standard Deviation

Sharpe Ratio in lowest to highest order:
GenM,Haio,NTPM,Pbbank,LPI

Excel Solver Constraints:
Constraint#1: optimized weightage <=1 Constraint#2: desired return per month = 2.5% Constraint#3: sum of optimized weightage = 1 Current invested or value weight:
GenM : HaiO : NTPM : PbBank : LPI = 0.21 : 17.2 : 25.6 : 51.9 : 3.2

Excel Solver optimized weightage:
GenM : HaiO : NTPM : PbBank : LPI = 0.58 : 19.56 : 15.44 : 33.02 : 31.4

Reference of Relocation from Method 1 optimization:
Strategy 1: reduce GenM weightage or sell off all
Strategy 2: reduce high weightage of Pbbank and NTPM
Strategy 3: increase LPI weightage

Action recommended:
1. Stop buying GenM, Pbbank and NTPM. Extra cash is used to buy HaiO and LPI. Second Method:
This is the second method which takes into account of standard deviation.
Variance stock i = VARP(Array stock i)
Covariance stock i to j = COV(Array stock i, Array stock j)

Variance Term stock i = Stock i weightage*SUMPRODUCT(Array weightage, Array COV or/and VARP)

Portfolio variance = Summation of all variance term stock
Portfolio standard deviation = SQRT(profolio variance)

Excel Solver constraint:
Constraint#1: Optimized weightage >=0
Constraint#2: desired retrurn = 2.5% per month
Constraint#3: sum of optimized weightage = 1





Current invested or value weight:
GenM : HaiO : NTPM : PbBank : LPI = 0.21 : 17.2 : 25.6 : 51.9 : 3.2
Current portfolio return: 2.05%
Current portfolio standard deviation: 4.13%
Current portfolio Sharpe ratio = (2.05-0.21)/4.13 = 0.4455

Excel Solver optimized weightage:
GenM : HaiO : NTPM : PbBank : LPI = 7.39 : 3.1 : 15.35 : 31.78 : 42.38
Optimized portfolio return: 2.5%
Optimized portfolio standard deviation: 2.03%
Optimized portfolio Sharpe ratio = (2.5-0.21)/2.03 = 1.128

Conclusion:
Method 2 has a big different perspective in relating risk and return relationship. Our common sense that applied at Method 1 is beaten down by the statistical approaches.

Method 1: GenM(hold), HaiO(increase), NTPM(decrease), PbBank(decrease), LPI(increase)
Method 2: GenM(increase), HaiO(decrease). NTPM(decrease), PbBank(decrease), LPI(increase)

Thanks to the Markowitz,s CAPM for a better understanding on the risk and return relationship.