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
Showing posts with label Solver. Show all posts
Showing posts with label Solver. Show all posts
Sunday, August 22, 2010
Tuesday, August 3, 2010
Overall Retirement Plan + Children Education Plan - Two Kids Plan
Mr. E aged 35 years old, plans to marry now and hopes to have two kids - 1st kid right after marry and 2nd kid one year after marry. What is the retirement fund and children education fund for the overall family plan?
Assumption:
1) His wife and Mr. E are same age
2) His wife and Mr. E plans to work till 60 years old
3) His hife has monthly RM500 EPF contribution with the beginning saving of RM40,000 at the Account I and Account II. EPF annual dividend is 6.0% p.a.
4) Mr. E's asset appreciation at pre-retirement rate of 10% p.a. while post-retirement rate of 8% p.a., salary increment at 5% p.a., cost of living inflation at 3.2% p.a.,
5) Children Education fees (school fees and living cost) RM25,000 p.a., inflation at 6% p.a., education fund performance at 8%. p.a.
6) Miscellaneous expenses: RM1,500 monthly for contingency reserve
Financial Planning approaches:
1) Target Replacement Ratio: 80%
2) Retirement fund calculation - principal liquidation
V@35 denotes Mr. E's value at current age while V@60 denotes Mr.E's value at retirement age. It has a negative net worth after the consideration of offsetting liabilities with the asset. Thus,
Mr. E has to plan some action for his retirement fund and children education fund preparation.
You can replace the Mr. E figures by yours. Check and see the result.
The previous result is based on the assumption 4, 10% p.a. for the net worth appreciation CAGR. What is the desired return that Mr. E required in order to have the net worth at RM 0?
By using solver, 11% p.a. CAGR is calculated. Thus, he needs to ensure that his asset appreciation must be over 11% p.a.
However, Mr.E required a house and a car ++ till 85 years old. So, the solver is re-simulated by reserving 395k@60 years old. Thus, he needs to ensure that his asset appreciation must be over 11.28% p.a.
After the study of his portfolio CAGR return, which is 13.2% p.a. When will be his financial freedom age?
From solver, his financial freedom age is 40 years old. Thus, he has to ensure his portfolio return can generate 13.2% p.a. CAGR every year till 85 years old.
Assumption:
1) His wife and Mr. E are same age
2) His wife and Mr. E plans to work till 60 years old
3) His hife has monthly RM500 EPF contribution with the beginning saving of RM40,000 at the Account I and Account II. EPF annual dividend is 6.0% p.a.
4) Mr. E's asset appreciation at pre-retirement rate of 10% p.a. while post-retirement rate of 8% p.a., salary increment at 5% p.a., cost of living inflation at 3.2% p.a.,
5) Children Education fees (school fees and living cost) RM25,000 p.a., inflation at 6% p.a., education fund performance at 8%. p.a.
6) Miscellaneous expenses: RM1,500 monthly for contingency reserve
Financial Planning approaches:
1) Target Replacement Ratio: 80%
2) Retirement fund calculation - principal liquidation
V@35 denotes Mr. E's value at current age while V@60 denotes Mr.E's value at retirement age. It has a negative net worth after the consideration of offsetting liabilities with the asset. Thus,
Mr. E has to plan some action for his retirement fund and children education fund preparation.
You can replace the Mr. E figures by yours. Check and see the result.
The previous result is based on the assumption 4, 10% p.a. for the net worth appreciation CAGR. What is the desired return that Mr. E required in order to have the net worth at RM 0?
By using solver, 11% p.a. CAGR is calculated. Thus, he needs to ensure that his asset appreciation must be over 11% p.a.
However, Mr.E required a house and a car ++ till 85 years old. So, the solver is re-simulated by reserving 395k@60 years old. Thus, he needs to ensure that his asset appreciation must be over 11.28% p.a.
After the study of his portfolio CAGR return, which is 13.2% p.a. When will be his financial freedom age?
From solver, his financial freedom age is 40 years old. Thus, he has to ensure his portfolio return can generate 13.2% p.a. CAGR every year till 85 years old.
Wednesday, June 2, 2010
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.
Tuesday, May 25, 2010
Investment Planning: Asset Relocation 4
4 types of believer views return-to-risk ratio.
1) Risk adverse - believe in risk free investment is the most secure investment in the universe.
Portfolio characteristic/Solver key constrains: lowest standard deviation

2) Risk taker - believe in high risk high gain and no risk no gain.
Portfolio characteristic/Solver key constrains: highest return, 100% concentration to one counter
3) Risk optimize - believe in statistical optimization in portfolio.
Portfolio characteristic/Solver key constrains: highest sharpe ratio, (averagereturnrate - riskfreerate)/standarddeviation
4) LUCK - believe in supernatural, windfall, random or trial-and-error
Portfolio characteristic: random, no plan or fortune teller.
Conclusion:
1) Risk adverse - believe in risk free investment is the most secure investment in the universe.
Portfolio characteristic/Solver key constrains: lowest standard deviation

2) Risk taker - believe in high risk high gain and no risk no gain.
Portfolio characteristic/Solver key constrains: highest return, 100% concentration to one counter

Portfolio characteristic/Solver key constrains: highest sharpe ratio, (averagereturnrate - riskfreerate)/standarddeviation

Portfolio characteristic: random, no plan or fortune teller.
Conclusion:
Portfolio Risk | Portfolio Return | Sharpe Ratio | |
Risk Adverse | 2.4% | 0.8% | 0.2479 |
Risk Taker | 12.6% | 6.1% | 0.4690 |
Risk Optimize | 3.8% | 3.3% | 0.8090 |

Labels:
Asset Relocation,
Investment Planning,
return,
risk,
Sharpe Ratio,
Solver
Tuesday, May 18, 2010
Investment Planning: Asset Relocation 3
1st Step: Collect historical adjusted price from Yahoo Finance. Adjusted price is the corrected price after considering the dividend and share split. You need to spend some time in evaluating the reliability of the adjusted price in the event of after share split.

Table 2: Variance and Covariance Matrix for the Portfolio
Step 2: Variance and covariance calculation.

3rd step: Calculation portfolio weightage. Then calculate Portfolio Return (current), Portfolio Return (optimized) and Sharpe Ratio.
Next time I will discuss about the implication of the model with different scenario.
Labels:
Asset Relocation,
Investment Planning,
Sharpe Ratio,
Solver
Saturday, May 8, 2010
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.
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
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.

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.
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