This presentation discusses dynamic asset allocation strategy and portfolio insurance. It begins by defining dynamic asset allocation as a strategy that continuously revises the proportions of a portfolio between an underlying asset and riskless asset to insure the portfolio's value and reduce fluctuation risks. The document then outlines the process of dynamic asset calculation, makes assumptions about the investment amounts and market data, and selects 10 companies across various sectors. It shows the portfolio returns and standard deviations for different quarters. The rest of the presentation calculates portfolio values using 100% equity, 50% risky/50% risk-free asset allocations, and determines put and call option values to calculate insured portfolio values and asset allocations on a quarterly basis. It concludes that dynamic asset allocation using

1. Welcome to the
Presentation

2. Md. Monjurul Ahsan
20-376

3. Portfolio Insurance and
Dynamic Asset Allocation
Strategy

4. Dynamic Asset Allocation
 A strategy where manager replicates an option through continuously revising the
proportions of a portfolio consisting of the underlying asset and the riskless asset
to insure portfolio’s value.
 The general premise of dynamic asset allocation is to reduce the fluctuation risks
and achieve returns that exceed the target benchmark.

5. Process of Dynamic Asset Calculation
1. Put
Option
Dynamics
2. Call
Option
3. Call
Option Delta
4. Insured
Portfolio
5. Asset
Allocation

6. Assumptions
 Investment amount is 1000000 Tk.
 Initial distribution of total fund between Risky securities and T-bills is considered to
be 50:50
 Price data and dividend data are collected mainly for the year 2017 Q4 to 2018
Q3, as I have considered investment horizon to be in the year 2017 Q4 to 2018
Q3.
 The amount of investment in shares will be distributed among the 10 securities
equally
 Continuous compounded risk free rate is assumed.
 Call and Put option strike prices are assumed 1080000 Tk.

7. Sector Company Face value
Bank AB Bank 10
Textile APEX SPINNING & KNITTING MILLS LIMITED 10
Engineering Aftab Automobiles 10
Pharmaceuticals IBNSINA Pharmaceuticals 10
Telecom GP 10
NBFI Lankabangla 10
Cement Lafarge Surma Cement 10
Fuel and power Jamunaoil 10
Ceramic RAK Ceramics 10
Food & Allied BATBC 10
SELECTED
SECURITIES

8. Dividend Adjustment on Daily Share Price
 Bonus Share Adjustment =
Previous Closing Price × (1+ bonus share rate)
 Cash Dividend Adjustment =
Previous Closing Price + (Face Value × % of cash dividend)

9. PORTFOLIO RETURN AND STANDARD
DEVIATION
Portfolio Return Standard deviation
Q4 (2017) 0.000122488 0.1475362
Q 1(2018) 0.00095636 0.0541576
Q 2(2018) -0.000641803 0.0832974
Q 3 (2018) 0.000740908 0.1297833

10. 100% Equity Portfolio
 As the initial investment is Tk. 1,000,000 so multiplying by the up factor value of up
can be made and multiplying by the down factor value of portfolio down can be
determined.
Q4 Q1 Q2 Q3
Initial value 1000000 1098878.7 1491352.6 1713456.9
Lowest value 1206132.528 1437472 1854192.6 2220940.2
Highest value 1228123.115 1462313.7 1877061 2256959.3
Closing value 1098878.739 1491352.6 1903841 2345349.8

11. Up and Down Factor Determination
Up factor, u = eσ√t
Down Factor, d = 1/u
The up factor and down factor for each quarter are as follows:
Quarters u d
Q4(2017) 1.13858149 0.878286
Q1(2018) 1.158975145 0.862831
Q2(2018) 1.055650897 0.947283
Q3(2018) 1.086864958 0.920078

12. Binomial Tree of 100% Equity
Portfolio

13. 50% Investment in Risky Assets
 This strategy tells the idea of investing 50% of the taka 10, 00,000 in risky assets
and rest in the risk free asset, T-bill
50% Investment In Risky Assets
Q4 Q1 Q2 Q3
Initial value 128,737.94 86,535.37 171,864.95 215,273.31
Lowest value 135,186.09 118,658.28 194,620.05 253,844.37
Highest value 162,564.92 92,825.66 211,169.23 255,390.58
Closing value 441,422.02 109,928.09 498,173.92 551,350.10

14. 50% Investment in Risk Free Assets
 50% of the initial amount has been allowed for risk free investment in the T-bill. T-
bill rate of 91 days varies among the quarters in the year.
50% T-Bill
Tenor
Quarter 4
(2017)
Quarter 1
(2018) Quarter 2 (2018)
Quarter 3
(2018)
oct-dec jan-mar apr-jun july-sep
91 Days T-Bill Rate 3.25% 2.97% 2.80% 4%
Continuous Compounding
Rate 1.008 1.007 1.007 1.010
Amount to be invested 5,000,000.00 5,040,790.49 5,078,357.65 5,114,030.8
Total Value 5,040,790.49 5,078,357.65 5,114,030.87 5,167,365.1

15. P value calculation
Through the determination of probability of the up and down value of put option, the
put option value can be calculated. Now for probability calculation the following
formula has been used:
Probability for up node, P = (a-d)/(u-d)
Probability for down node (1-P)
Here, a= er∆t
u d a p (1-p)
Q4(2017) 1.13858149 0.878286 1.032898 0.593988 0.406012
Q1(2018) 1.158975145 0.862831 1.030032 0.564594 0.435406
Q2(2018) 1.055650897 0.947283 1.028295 0.747568 0.252432
Q3(2018) 1.086864958 0.920078 1.042150 0.731906 0.268094

16. Call Option Dynamics

17. Put Option Dynamics
Put option value = e-rt × (portfolio up × p +portfolio
down×1-p)

18. Delta calculation
The number of units of the underlying portfolio that must be held long at any given
moment will be given by the call option “Delta”, the reciprocal of how many calls it takes
to hedge the unit of the underlying portfolio. The call delta tells us the number of units
of the underlying portfolio to hold.

19. Call Option Delta
 ∆= (𝒇𝒖 − 𝒇𝒅)/(𝑺𝒐𝒖 − 𝑺𝒐𝒅)

20. Allocation of the Portfolio
Initial amount of investment is 10,00,000 tk. I have allocated 100% equity
in Dynamic Asset Allocation. I have started dynamic allocation by using
insured portfolio of put option as our initial insured portfolio. Then from
each quarter I have calculated the insured portfolio by multiplying the
100% equity with the call Delta of the previous quarter. If that present
quarter’s delta is greater than that of previous quarter I have bought
stocks and T-bills have been sold of the same amount. Then by multiplying
the 100% equity of each quarter with that present quarter delta I have got
how much equity to hold in our new portfolio and the rest to hold T-bills. I
have allocated the equity and T-bills in each quarter continuously in this
way.

21. Insured Portfolio
Insured Portfolio is found through summing up each node
of portfolio dynamics and put option dynamics.

22. Dynamic Asset Allocation
100% Equity portfolio 1000000
Insured portfolio 1067368
Initial Delta 0.647382
New Portfolio
Shares (0.843127*1000000) 647381.7
T-bill 419986.7
Total 1067368
Quarter 0
100% Equity portfolio 878285.8
Insured portfolio 1012610
Shares (0.84313*942285) 568586.2
T-bill 444023.9
Total 1012610
New Delta 0.181739
Sell (0.3693*942285) Shares 408967.5
Buy T-bill 408967.5
New Portfolio
Shares (0.47383*942285) 159618.7
T-bill 852991.4
Total 1012610
Quarter 4b (2017)
100% Equity portfolio 1138581
Insured portfolio 1161105
Shares (0.84313*1061250) 737096.9
T-bill 424007.9
Total 1161105
New Delta 0.898707
Sell (.097526102*1061250) Shares 286154
Buy T-bill 286154
New Portfolio
Shares (.94065*1061250) 1023251
T-bill 710161.8
Total 1733413
Quarter 4(2017)

23. Comparison
1. Static Portfolio
2. 100% T-Bill Portfolio
3. 100% Equity Portfolio
4. Dynamic Portfolio

24. Comparison in terms of absolute
portfolio Value
0
200000
400000
600000
800000
1000000
1200000
1400000
1600000
Q4 (2017) Q1 (2018) Q2 (2018) Q3 (2018)
Absolute portfolio Value
Static Portfolio 100% T-Bill portfolio 100% equity Portfolio Dynamic Portfolio

25. Comparison in terms of absolute return
-20.00%
-10.00%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
Q4 (2017) Q1 (2018) Q2 (2018) Q3 (2018)
Return on investment
Static Portfolio 100% T-Bill portfolio 100% equity Portfolio Dynamic Portfolio

26. Comparison in terms of Q2Q return
-20.00%
-15.00%
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
Q4 (2017) Q1 (2018) Q2 (2018) Q3 (2018)
Q2Q Return
Static Portfolio 100% T-Bill portfolio 100% equity Portfolio Dynamic Portfolio

27. Conclusion
 Portfolio insurance provides a way out how the risk can be minimized using the
replications of options. This strategy has been proved worthy of using for specially
risk averse investors.
 Delta value has been important to hold the number of risky assets. Then, we can
determine the holding of investment in T bill as rest of the investment happens in
the stock.

28. THANK YOU