Development of New Persistency Values and Analysis of Equity

to Optimize Company Profit

By

Monica E. Revadulla

A FINAL REPORT

In partial fulfillment of

The requirements for the

Internship and Degree of

BS Applied Mathematics

Actuarial science

submitted to

Mr. Jonathan B. Mamplata

Adviser/Assistant Professor 1

University of the Philippines Los Banos

May 21, 2013

ABSTRACT

The internship was taken at First Life Financial Co. Inc, Office of the Actuary, 7th Floor,

First Life Center, 174 Salcedo St., Legaspi Village, 1229 Makati City, Philippines. The primary

objective was to propose a new set of persistency ratios based on the comparison and analysis

between the current and experienced persistency values of the year 2012, with the 2012 database

as basis, which would be recommended to be the current persistency for the year 2013. Various

useful hotkeys and macros in Excel were learned every day and the importance of an accurate set

of qx for the profit generation of the company was emphasized. The secondary objective was to

propose a tabular schedule of the purchase time of PSEI stocks and selling time of First Life stocks.

An optimal schedule must be obtained to ensure profitability of the trade, and was done by a trend

analysis of all stocks for forty days, using formulas by Markowitz and Wilder.

TABLE OF CONTENTS

Abstract i

Scientific Report: Persistency 1

Introduction 1

Materials and Methods 1

Results 2

Summary 2

Scientific Report: Equity 3

Introduction 3

Materials and Methods 3

Results 4

Summary 4

List of Figures 5

Insights 8

Suggestions 9

1

Scientific Report (Persistency)

I. Introduction

In order to maximize the profit and to ensure that benefit premiums are available and

not overflowing at the end or termination, a new set of persistency values would be computed.

The data needed would be taken from the database containing all policies that are active on the

year 2012 of First Life Co., Inc, both local and international policies. The study aims to

maximize the profit and minimize the over estimation of benefit reserves per policy year.

II. Materials and Methods

Microsoft Excel

The raw policy database, containing necessary personal (name, birth date), and

account information (policy number, insurance type, status code, premium

amount, issue date and due date, mode of payment, beneficiary, plan code) of

all policyholders for the year 2012 was given, together with the list of plan

codes with their corresponding plan names.

The raw database was filtered. Policies which status codes given below are

excluded:

o CANC Cancelled

o CONV Converted

o DTH A/D/P/S Death

o NTU Not Taken Up

o WPPA Withdrawal

The following are the necessary account information needed for the

computation. The filtered database is shown in Figure 1.

o Policy Number

o Currency (PHP, USD)

o Plan Code

o Start Date

o STS Code

o Due Date

o Mode of Payment

o Premium

o Pay period of policy

The earliest policies were bought at year 1989 and would terminate at year

2012. So, year of valuation for the entire duration would be 23 years. As shown

in Figure 2, under year 1. If start year of policy plus year of valuation is less

than or equal to the end year, the premium paid would be recorded as income,

while if start year of policy plus year of valuation is greater than end year, no

premium would be recorded since the contract is already terminated.

The exposure is computed by summing all fixed annual premiums paid for the

specified n-pay plan, regardless of termination of contract, while the inforce is

2

computed by summing all fixed annual premiums paid on the year of valuation

itself, taking into consideration the termination of contract.

o For the exposure of 5-pay for the year 2010, third year of valuation (3),

sum all premiums with 5-pay as plan codes, where the start year of

policy is equal to 2010- 3-1. The subtrahend 1 is a constant for all

exposure formulas.

o For the inforce of 5-pay for the year 2010, third year of valuation (3),

sum all premiums under the third year of valuation with 5-pay as plan

codes, where the start year of policy is equal to 2010-3-1.

Another sheets for the summary of experienced persistency values is created,

each sheet corresponding to each n-pay plan code. For this database, we have

single pay (1-pay), 5-pay, 10-pay, etc. The persistency is computed by

inforce/exposure, and the average of the values for all n-pay for all policies are

taken, which would be compared to the current persistency.

The current persistency values are also included in the database. The plan codes are sorted by n-pay. The most common persistency pattern found for all plan

codes would be the one compared to the experienced persistency.

The current persistency values were taken under linear interpolation and exponential interpolation, where the two points are (1, initial persistency) and

(n-pay, final persistency). Since the goal is to have the values closer to the

experienced values, the user would be given the choice to input the desired

initial and final values.

III. Results

Figure 3 shows the results of the experienced values for the 5-pay plan codes for the

year 2012. The years would extend up to 2003 to ensure more than five years of historical data

are studied. Figure 4 shows the found values after taking the average of 5-years of experienced

persistency. Figure 5 shows the sorted plan codes by n-pay.

IV. Summary

On average of the experienced persistency values, a 10% initial persistency was found,

which is too far for the 20% current persistency value. In order to meet ends, the middle, 15%,

was the value decided to be recommended to the Chief Actuary, since the 15% value array was

close enough to the 10%, in comparison to the current 20%.

3

Scientific Paper (Equity)

I. Introduction

In order to maximize profit by minimizing cost on undervalued stocks and investing a

an amount of money on rising stocks, a tabular schedule of the purchase time of

Philippine Stock Exchange Inc., (PSEI) stocks and selling time of First Life stocks

would be proposed. An optimal schedule would be obtained to ensure profitability of

the trade, by analyzing stocks for an average of forty days in the methods of Markowitz

and Wilder.

II. Materials and Methods

Microsoft Excel

Summary of owned stocks of First Life

o Company name

o Number of shares

o Cost per share

o Total cost

PSEI website

Create two workbooks, one for stocks to buy and one for stocks to sell. Create

a sheet for each stock, and rename it by the stock code (found at PSEI website)

In Microsoft Excel,

o Merge cells A1 until M1, input company name.

o Merge cells A3 and A4, input Date; B3 and B4, Time (t), C3 and

C4, Stock Price (St); D3 and D4, Return; H3 and H4, Advance;

I3 and I4, Decline.

o Merge F2 and G2, K2 and L2, input Exponential Moving Average.

o Merge H2 and I2, input Relative Strength Index.

o On F3, 12-day, on G3, 26-day. On K3, 14-day Advance, on L3,

14-day Decline.

o On M4, input RSI.

The values below represent k for the whole column.

o On F4, =2/(VALUE(LEFT(F3,2))+1),

o On G4, =2/(VALUE(LEFT(G3,2))+1)

o On K4, =2/(VALUE(LEFT(K3,2))+1)

o On L4, =2/(VALUE(LEFT(L3,2))+1)

Go to the PSEI website and input corresponding dates, time and stock prices.

Simply input the company code in the search tool of PSEI, go to the Historical

Data tab, and copy stocks under the close column.

Returns are computed as S(t)/S(t-1).

The Exponential Moving Average (EMA) is computed as ((S(t)-EMA(t-

1))*k)+EMA(t-1). Do these for columns F, G, K, and L. Initial EMA for F and

4

G is the stock price at time 1, while for K and L, RSI for Advance and Decline

at time 2, respectively.

The Relative Strength Index for Advance simply measures the increase of stock

price, while Relative Strength Index for Decline measures decrease of stock

price. If stock price increased, RSI for Decline has no value, and vice versa.

The RSI at Column M has the formula RSI (t)=1 1

1+ ()

()

.

Create another sheet for Fibonacci Retracements. Compute Target Price, stop-

gain and stop-loss. Use 0%, 23.6%, 38.2%, 50%, 61.8%, 75% and 100% as

targets.

Graph the Stock Price, EMA for 12-day and 26-day against time. Place the

Fibonacci Retracements as guidelines along the x-axis.

For the tabular schedule, get the last recorded RSI of all stocks to be bought,

arrange it in ascending order. Get the last recorded RSI of all stocks to be sold,

arrange it in descending order. Do these in another sheet. Assuming that the

cost of all sold stocks would be equal to your buying cost, its easier to buy and

sell simultaneously.

III. Results

Figure 7 shows some of the results of the Universal Robina Corporation (URC) stock

trend. The fact that the 12-day EMA trend is higher than the 26-day EMA trend

signifies the stock performs better on a short-term basis than long term. Normally, RSI

at time 1 and 2 would not exist. The graph would also help the user to monitor the stock

trend in an easier manner. The graph of URC is shown at Figure 8.

The results of the proposed tabular schedule are on Figure 9. Note that the Relative

Strength Index is prone to changes every day, so the order of the stocks would change.

Simply relate the cells to each other to ease this problem.

IV. Summary

Wilders development of the Relative Strength Index made it easier for a stock watcher

to monitor the stock trend. It is a criteria that proved itself useful over the years.

5

LIST OF FIGURES

Figure 1. Filtered 2012 database primarily used throughout the computation of qx

Figure 2. Summary of received premiums per year

NUM CUR CODE POLDTE STSCODE POL ANIV POLFRQ PREMIUM ann_prem_if pay period P_year e_year

3 PHP 1850 9-May-89 LAPSED 9-May-03 2 4487.81 0.00 0 1989 2002

4 PHP 1200 16-May-89 PUP 16-May-10 1 3761.09 3,761.09 20 1989 2009

8 PHP 1850 23-May-89 PPP 23-May-13 1 605.85 0.00 0 1989 2012

10 PHP 1989 23-May-89 PUP 23-May-13 1 132300 132,300.00 99 1989 2012

16 PHP 2600 27-Jun-89 PPP 27-Jun-13 1 1409.1 0.00 0 1989 2012

20 PHP 1200 11-Jul-89 PUP 11-Jul-09 1 3562.65 3,562.65 20 1989 2008

24 PHP 2600 19-Aug-89 PPP 19-Aug-12 1 665.28 0.00 0 1989 2011

28 PHP 1850 15-Sep-89 PPP 15-Sep-11 1 25347 0.00 0 1989 2010

38 PHP 1200 25-Sep-89 LAPSED 25-Sep-02 2 10080 20,160.00 20 1989 2001

NUM

3

4

8

10

16

20

24

28

38

P_year e_year 1 2 3 4 5

1989 2002 0.00 0.00 0.00 0.00 0.00

1989 2009 3,761.09 3,761.09 3,761.09 3,761.09 3,761.09

1989 2012 0.00 0.00 0.00 0.00 0.00

1989 2012 132,300.00 132,300.00 132,300.00 132,300.00 132,300.00

1989 2012 0.00 0.00 0.00 0.00 0.00

1989 2008 3,562.65 3,562.65 3,562.65 3,562.65 3,562.65

1989 2011 0.00 0.00 0.00 0.00 0.00

1989 2010 0.00 0.00 0.00 0.00 0.00

1989 2001 20,160.00 20,160.00 20,160.00 20,160.00 20,160.00

Persistency (5-Pay)

Exposure 1 2 3

2010 8517382 15135102 13603346

2009 15135102 13603346 7460492

Inforce 1 2 3

2010 7786013 15001169 13009001

2009 15032188 13155165 6782981

Persistency 1 2 3

2010 91.41% 99.79% 98.89%

2009 99.32% 99.70% 99.54%

6

Figure 3. Experienced persistency results for all 5-pay plan codes

Figure 4. The resulting qx for 5-pay plan codes

Figure 5. Current plan codes sorted through n-pay

95.2% 99.5%

4.8% 0.5%

h-pay Plan Code 1 2 3 4

1205, 1206, 2520, 2620, 2882 20.00 9.00 4.00 3.00

1995, 1996 19.67 8.95 4.00 3.00

2105 12.00 8.00 4.00 3.00

2125, 2135, 2165, 2175 19.67 8.95 4.00 3.00

7-pay 2127, 2157, 2167, 2207 15.00 7.50 5.00 2.50

1102 19.67 8.95 4.00 3.00

1201, 1202, 1960, 1965, 1999,

2060, 2065, 2120, 2220, 2883 20.00 9.00 4.00 3.00

1997, 1998 19.67 8.95 4.00 3.00

2202 12.00 8.00 4.00 3.00

3100, 3101 20.00 15.00 15.00 12.00

15-pay 1915, 1916 20.00 9.00 4.00 3.00

20-pay 2200 20.00 9.00 4.00 3.00

1900, 1901, 1990, 1992 20.00 9.00 4.00 3.00

1989 19.67 8.95 4.00 3.00

5 - pay

10-pay

99-pay

lin15

x 5 7 10 15 20 99 15.00

1 15.00 15.00 15.00 15.00 15.00 15.00 1.00

2 11.50 12.67 13.44 14.00 14.26 14.86

3 8.00 10.33 11.89 13.00 13.53 14.71 x1 y1 x2 y2

4 4.50 8.00 10.33 12.00 12.79 14.57 5 1.00 15.00 5.00 1.00

5 1.00 5.67 8.78 11.00 12.05 14.43 7 1.00 15.00 7.00 1.00

6 3.33 7.22 10.00 11.32 14.29 10 1.00 15.00 10.00 1.00

y

Input Initial Persistency:

Input Final Persistency:

7

Figure 6. Results of the linear interpolation for a 15% initial persistency

Figure 7. Monitoring stocks of the Universal Robina Corporation

Figure 8. Graph of URC stocks

Figure 9. The tabular schedule of buying and selling of stock

12-day 26-day 14-day Advance 14-day Decline

k= 0.153846154 0.074074074 k= 0.133333333 0.133333333

4-Mar-13 1 PHP 93.95 PHP 93.95 PHP 93.95

5-Mar-13 2 PHP 96.50 0.02678 PHP 94.34 PHP 94.14 PHP 2.55 PHP 0.00 PHP 2.55 PHP 0.00 #DIV/0!

6-Mar-13 3 PHP 97.50 0.010309 PHP 94.83 PHP 94.39 PHP 1.00 PHP 0.00 PHP 2.34 PHP 0.00 #DIV/0!

7-Mar-13 4 PHP 96.00 -0.0155 PHP 95.01 PHP 94.51 PHP 0.00 PHP 1.50 PHP 2.03 PHP 0.20 91.03%

8-Mar-13 5 PHP 97.00 0.010363 PHP 95.31 PHP 94.69 PHP 1.00 PHP 0.00 PHP 1.89 PHP 0.17 91.61%

RSIAdvance DeclineReturnStock Price (St)Time (t)Date

Exponential Moving Average Relative Strength Index Exponential Moving Average

Buy Sell

RSI RSI

37.03% FGEN loss>gain 69.94% OPMB gain>loss

37.66% EDC loss>gain 62.98% GLO gain>loss

57.50% PGOLD gain>loss 62.03% SMC2C gain>loss

8

Insights

Its worthwhile to enumerate everything Ive learned from the company and the university

acquired skills I used, since needless to say, they are quite many.

Microsoft Excel hotkeys. Ive always been holding on to my mouse whenever I use

MS Excel until now, thanks to all the keyboard shortcuts Ive learned all the way,

which proved to save time. A lot.

Macro. Ive never been a fan of programming: I passed FORTRAN and Scilab with

lots of prayers and help from friends. But whoa, when I was faced with a

programming task (I even think Sir gave it to me on a learning purpose since he

knows I hate programming), I felt as if I was doing this for a very long time. My

mind accepted the alien codes and information: it even looked for more!

Admittedly, I enjoyed it. =D ganun pala ka-fun mag program. Maximizing what you have. The boss wants this output. He gives you two inputs,

but you need five. You ask but he just smiles. Thus, its up to you on how to work

with the two in order to get the other three.

Punctuality. Lets face it: most professors in the university dont give much thought

to students who are late in their class (except for the first month, maybe), moreover

to students who are having so much fun maximizing the number of absences. One

cant really blame them, since its not worth the time noting down or reprimanding

every student who gets beyond the grace period. Because of that, students tend to

have the annoying ability to come to class late. Unfortunately, I brought that attitude

with me, but because of the biometrics machine, I was trained for six weeks to come

to the office earlier than usual, and Im hoping I can bring that with me in school.

Dressing up. The university doesnt care what you wear to class, as long as it still

covers the parts that need to be covered, and needless to say, I brought that attitude

with me. It took a greater deal of focus and stress to choose the correct blouse-jean-

heels combination every night before going to bed.

A smile and a good morning. Once people get used to their daily routines at work,

they forget to wear a smile and greet everyone a good morning (except those at the

front desk). A fixed smile and a good morning for ten minutes from the front door

up to your office wont hurt, and its satisfying to put a smile on their face before

they face their jobs. Hindi ako ganun sa elbi (sa dami ng tao) but still, its worth it.

Work Fast. Faster! The boss sets a timeframe for deadlines, and as of your current

pace, he seems to go along with it well. Still, one cant shake off the nagging feeling

that you still have to work faster, and when you do, youll see a satisfied expression,

as if he expects you to finish it at an earlier time.

Speak English. Its undeniable: the English training you get from the university,

whether you felt it or not, is very useful outside, especially when talking to the

bigger bosses: the Chief Actuary for example.

9

Suggestions

MS Excel and Macro. It would greatly benefit the student to take a subject

focused on exercises which would make the student be used to shortcuts when

it comes to Excel. Nothings wrong with FORTRAN and Scilab, but Macro is

easier to understand since the language is more humanely understandable, thus

giving the programmer the feel of actually talking to the computer. If this is

somewhat too small for a 3-unit course, maybe discussing a chapter of it in

laboratory programming courses would help the student for internship.

Show real actuarial world applications of useful theoretical topics. The

persistency I was given was simply a qx turned more complicated, but all the

same. The premium pricing task were done using formulas which can be found

in 171 and 172 notes. Future interns would have a faster grasp of the application

of key concepts in their tasks if their sense in real world problems are more

elaborately discussed. The cash flow shown in 172 helped a lot, since a cash

flow was the first excel file I was shown. It was amusing to understand the cash

flow after some analysis but hard to create a new qx even after a week, given

that a qx is simpler. Im not sure if a one-hour laboratory class for 171 and 172

would greatly help, but Im still suggesting it.

Stress the importance of actuarial exams. Passing the actuarial exams is an

undeniable need for an actuary to reach ultimate success. For three years in the

BSAM course, nobody from my classmates felt the need to take even one exam

before graduating, or some did but wasnt fully decided on it. AS students from

other countries are required to be an associate actuary before graduation, while

its known that students from Ateneo and UST produced graduates with

actuarial exams. Theres a chance to further enhance the quality of actuarial

science graduates of UPLB if they would really feel the necessity to take exams

in college.