A Genetic Algorithm Approach to Optimal Asset Allocation of Defined Contribution Pension Funds: Evidence From India’s National Pension System

Abstract

Life cycle asset allocation has recently gained popularity and is the default option in pension funds worldwide. A line of recent studies has refuted its glory and argues that a balanced fund with a fixed allocation throughout the investment horizon may yield better results. The question arises from these studies: What should be the balanced fund’s optimum asset allocation weight? Therefore, the present study uses Genetic Algorithm to obtain the optimum asset allocation weight for India’s defined contribution pension plan subscribers. To validate our result, the study compares the results of a Genetic Algorithm to the outcomes of widely used asset allocation techniques, notably the life cycle and equally weighted strategies. This study holds important policy implications as, given the size of the pension asset and the long investment duration, even a trivial increase in return will substantially impact investment outcomes, affecting the subscribers’ well-being in old age.

Keywords

asset allocation defined contribution pension plan genetic algorithm life cycle fund National Pension System H55 H75 I38 J26 J32

Introduction

An increasing fiscal burden and rising life expectancy paired with low birth rates poses a substantial challenge to many countries’ government-run pay-as-you-go pension schemes. Therefore, there has been a global transition from a defined benefit (DB) pension system toward a defined contribution (DC) pension system (Consiglio et al., 2015; Forsyth & Vetzal, 2019; Gerrans & Clark, 2013). While Pension pay-out under the DB was predetermined based on the number of years of service and average earnings, the DC pension scheme determines the pension benefit based on the total contribution made by the employer and the employee and the net interest created on it (Blake et al., 2014; Dyachenko et al., 2022; Kurtbegu, 2018). Under the DC pension system, subscribers bear the responsibility of risk and return associated with the asset allocation decision (Boulier et al., 2001; Cairns & Parker, 1997). Asset allocation decisions are critical for DC subscribers as they affect the return on the fund portfolio, which in turn affects the retirement savings (Defau & De Moor, 2018; Gallo & Lockwood, 1995; Ibbotson & Kaplan, 2000; Sehgal & Pandey, 2012; van Heerden & Koegelenberg, 2013; Yoon, 2010).

Every subscriber under the DC plan is a long-term investor who makes decisions for at least 30–40 years during the accumulation phase and faces two central asset allocation dilemma that needs to be resolved: (I) what should be the optimal asset mix at a specific point in time? and (II) how should it change depending on the investment horizon and, therefore, the age of the investor? (Booth, 2004). However, due to the lack of financial literacy and an inability to understand the pension plan, most pension participants either make wrong decisions or opt for a default pension plan in which asset allocation is fixed based on the participant’s risk aversion (Antolin, 2010; He & Liang, 2015).

Life cycle asset allocation strategies have recently gained popularity and are set as default choices among pension plans globally. The popularity of the life cycle strategies is based on the fact that it simplifies the investment decision for the subscriber lacking financial knowledge or who finds difficulty choosing among different asset alternatives (Basu & Drew, 2009; Forsyth et al., 2019; Graf, 2016). Once selected, the subscriber is set free from the asset allocation decision throughout the investing period. The idea of life cycle asset allocation investing is that it shifts allocation from the highly volatile asset to the low volatile asset as the retirement date approaches. It provides high portfolio growth during the initial years and protects the accumulated wealth during the later years (Ciurilă et al., 2022; Creedy et al., 2015; Forsyth et al., 2019; Jimenez-Martin & Sanchez Martin, 2007; Khemka et al., 2021; Lewis & Okunev, 2009).

Recent research has argued that this strategy could be counterproductive since the life cycle strategy invests heavily in equity when the contribution size is small and slowly shifts to low-return assets when the contribution and the accumulated asset amount grow larger. Thus, the investor may forego the opportunity to earn higher returns on an enormous sum of money invested (Basu & Drew, 2009; Basu et al., 2011; Blake et al., 2014; Lewis, 2008a, 2008b; Pang & Warshawsky, 2010; Spitzer & Singh, 2008, 2011). Their findings have concluded that balanced funds that keep their asset allocation fixed throughout the investment period and maintain high equity allocation tend to dominate the outcome of all other life cycle funds.

In India, life cycle funds account for all assets under the National Pension System (NPS) and therefore raise concern about the adequacy of retirement benefit under it. Research on pensions in India has mainly focussed issues relating to ineffectiveness of the social security system, poor pension coverage, rising old-age poverty, the inadequacy of current pension pay-outs and pension literacy (Asher, 1996, 1998, 2008; Bali, 2014; Bharati & Singh, 2013; Bhardwaj et al., 2006; Dave, 2006; Ghosh, 2022; Goswami, 2001; Jha & Bhattacharyya, 2010; Kavishwar, 2022; Murari, 2020; Nanda, 2018; Rajasekhar et al., 2016; Sadhak, 2009; Sane & Thomas, 2014; Sanyal et al., 2011; Sanyal & Singh, 2013; Shah, 2003, 2005; Shankar & Asher, 2011; Singh et al., 2015; Thomas, 2000). In particular, Shah (2003) has explored the investment risk in the Indian pension in general and suggested the role of guaranteed in pension finance. Sane and Price (2018) in their paper have introduced a new model called ‘penCalc’ for simulating pension income scenarios in India’s National Pension System. Murari (2020) evaluated the performance of Pension Fund Managers (PFMs) under different National Pension System (NPS) schemes in India using risk-adjusted performance measures such as Sharpe, Treynor and Jensen’s alpha. However, there is dearth of research on retirement savings or asset allocation decisions in India. Additionally, what should be the optimum asset allocation weight of balanced fund that would maximize the retirement wealth of the DC subscribers in India is not known. Therefore, the aim of this study is to bridge this research gap by deriving the optimum asset allocation weights for the DC subscribers in India so that the wealth of the subscribers’ is maximized at the time of their retirement.

In this study, we have derived the optimum weights through the application of a Genetic Algorithm (GA) due to its ability to effectively address the complexities and uncertainties inherent in optimizing asset allocation decisions for the defined contribution (DC) pension system (Katoch et al., 2021; Senel et al., 2008). Asset allocation problems often involve non-linear relationships between variables, which can be challenging for other optimization techniques. GA’s metaheuristic algorithm can navigate non-linear relationships more effectively, allowing it to capture the complex interactions between asset classes and investor preferences (Mirjalili, 2019). Again, one of the key strengths of GA is its capability to overcome local optima. Traditional methods, such as gradient-based optimization, may converge to local solutions that appear optimal in a restricted region but fail to explore the broader solution space. GA, on the other hand, utilizes a population-based approach that explores a diverse set of solutions, increasing the likelihood of identifying the global optimum. GA inherently explores different asset allocation scenarios by generating a population of potential solutions and iteratively refines them through selection, crossover and mutation processes. This exploratory power enables GA to search a wide range of potential solutions and identify promising allocation weights (Katoch et al., 2021). Furthermore, Genetic Algorithm (GA) has been proven by various studies to give better result as compared to other methods used for optimization (Chang et al., 2009; Chou et al., 2017; Fahria & Kustiawan, 2021; Fu et al., 2013; Joo et al., 2005; Kalayci et al., 2017; Kantar & Ilhan, 2015; Lim et al., 2020; Lin & Gen, 2007; Oh et al., 2006; Samanta et al., 2006; Sarijaloo & Moradbakloo, 2014; Wang et al., 2019). By employing GA, this study can provide a robust and well-informed asset allocation strategy, ensuring that pension plan subscribers in India maximize their retirement wealth and achieve better financial security in their post-retirement years.

The remainder of the paper is organized as follows: The Pension Outcome Modelling for DC Pension Plan Subscribers section provides a description of the modelling of the India’s DC pension plan along with the asset allocation strategies in our research. The Empirical Result section describes the empirical results obtained. The Discussion and Conclusion section concludes our study providing research implication. The Limitation of the Study and Scope for Future Studies section states the limitation of the study and scope for future studies.

Pension Outcome Modelling for DC Pension Plan Subscribers

The study takes into account the situation of a fictitious worker who is saving for retirement. Retirement savings growth over time is influenced by a variety of socioeconomic variables as well as asset returns (Lewis, 2008a, 2008b). Therefore, we assume that a subscriber enrol in a pension plan at the age of 25 without bringing a transfer value from prior plan and retire at the age of 60 as such the subscriber has 35 years to retirement (Lewis, 2008b; Spitzer & Singh, 2008). The initial monthly wage is assumed to be $365.45 (Rs 30000). Taxation is not evaluated; hence, contributions and investment income are considered to be tax-free. We also assume yearly nominal wage growth of 8% (Statista, 2022) and annual pension fund contributions of 24% of gross salary (contribution under National Pension System). The annuity rate has been taken at 3% (LIC, 2022). The average life expectancy of a person at age 60 in India is taken as 18.8 years (UN, 2019). Additionally, we consider that all variables are expressed in nominal terms.

Financial Historical Data

The subscriber to the pension plan may choose three underlying assets: a riskless asset (a government bond), a moderately risky asset (a corporate bond) and a risky asset (equity). The three asset classes used for this study comply with Indian Pension Fund Regulatory and Development Authority (PFRDA) regulations. The Nifty 50 indexes (NSE, 2022) and S&P BSE India Corporate Bond Index (BSE, 2022) has been used as a proxy for equity and corporate bond asset class. The data for government bonds has been taken from 10 years’ yield of an Indian government bond (Investing.com, 2022). The study uses asset class data from January 2012 to December 2021. The decision to initiate the study in 2012 is supported by the availability of annual reports from PFRDA in the public domain on its website, which begin from that year. By utilizing data from 2012, the study ensures reliability and comparability for stakeholders, including subscribers and policymakers. This justifiable timeframe aids in offering meaningful insights and informed decision-making. The expected annual return of all three asset classes has been calculated using the following formula

A n n u a l r e t u r n (R_{e}) = Ln (\frac{P_{t}}{P_{t - 1}})

(1)

where

P_{t}

is the closing price of the current year and

P_{t - 1}

is the closing price of the immediately preceding year.

Tables 1 and 2 display the descriptive statistics for the total annual return for each asset class and the covariance matrix between the asset class. It is noted that historical data may not be a necessary reliable indicator of predicted returns in the future. Thus, the choice of data period and data type may impact the outcomes.

Table 1.

Descriptive Statistics of All Three Asset Classes (2012–2021).

	Equity	Corporate Bond	Government Bond
Arithmetic mean	.132250^a	.095130	.073606
Median	.126216	.095100	.074464
Minimum return	−.041456	.062600	.060613
Maximum return	.272985	.133600	.085551
Standard deviation	.110329	.026020	.008786

Source: RBI (2022), and S&P Global (2022).

^aSix places decimal points have been taken for more accurate calculation.

Table 2.

Covariance Matrix Between the Asset Classes.

Asset Class	Equity	Corporate Bond	Govt. Bond
Equity	.012200	.000554	−.000044
Corporate bond	.000554	.000677	.000051
Govt. bond	−.000044	.000051	.000077

Source: Authors calculation.

Pension Accumulation

The level of the accumulated fund at age t, denoted by $f_{t}$ , is given by

f_{t} = (f_{t - 1} + c * y_{t - 1}) (1 + R W)

(2)

where

f_{t}

denotes the fund at time t,

c

denotes the fixed contribution rate payable annually in advance,

y_{t - 1}

is the labour income received at age (t−1),

W

is the portfolio weight vector and

R

the vector of real (gross) asset returns.

The retirement income from the age of 61 can therefore be obtained through the following formula

A n n u a l r e t i r e m e n t i n c o m e = \frac{f_{f i n a l}}{P r e s e n t v a l u e o f w h o l e l i f e a n n u i t y}

(3)

where

P r e s e n t v a l u e o f w h o l e l i f e a n n u i t y = \sum_{t = 0}^{m} t P_{x} V^{k}

(4)

where m is the maximum age,

t P_{x}

is the probability that a retiree of age x (at retirement) survives for t years and v is the discount factor based on the low-risk asset’s return.

The net replacement ratio, rather than the final fund, is more important to the retiree since the final accumulation is intended to be converted into an annuity. Therefore, the net replacement ratio is the proportion of retirement income to final payment.

N e t r e p l a c e m e n t r a t i o = \frac{A n n u a l R e t i r e m e n t i n c o m e}{F i n a l s a l a r y}

(5)

However, the replacement rate is solely applicable to government and private sector employees. The replacement rate should be ignored for subscribers who are not regular paid workers as the stable wage rate may not be possible for workers in the informal sector.

Asset Allocation Practices and Genetic Algorithm

Life Cycle Strategy and National Pension System

In India, with the introduction of a National Pension System (NPS) in 2004, which is of DC type, the life cycle model has been set as the default option for asset allocation on the recommendation of the newly formed Pension Fund Regulatory and Development Authority (PFRDA). The National Pension Schemes provide the Subscriber ‘Auto’ and ‘Active choice’. When the Subscriber fails to make any active choice or chooses Auto choice, the Asset of its Subscriber is allocated under Auto choice (default) as a Life cycle strategy based on their age (PFRDA, 2022).

The PFRDA has established standards for the maximum and minimum exposure of life cycle funds to each of the three asset classes – equities, corporate bonds and government bonds, which would change as per the age of the Subscriber. The life cycle fund offers three distinct allocation methods, aggressive, moderate and conservative, which are based on age and the risk appetite of the subscriber.

Each life cycle asset allocation strategy is detailed in Table 3. The starting asset allocation as a percentage allocated to equity, corporate bond and government bond under aggressive, moderate and conservative life cycle funds are 75/10/15, 50/30/20 and 25/45/30, respectively. Similarly, the ending asset allocation as a percentage allocated to equity, corporate bond and government bond under aggressive, moderate and conservative life cycle funds are 15/10/75, 10/10/80 and 5/5/90, respectively. All three life cycle funds have a glide path of 20 years.

Table 3.

Life Cycle Funder Under NPS.

Life Cycle Fund	Starting Asset Allocation^a	Ending Asset Allocation^a	Glide Path
Aggressive life cycle fund	75/10/15	15/10/75	20 years
Moderate life cycle fund	50/30/20	10/10/80	20 years
Conservative life cycle fund	25/45/30	5/5/90	20 years

Source: PFRDA (2022).

^aShown as a percentage allocated to equity, corporate bond and Government bond, respectively.

Since the weights for these strategies are predefined and established based on the NPS subscriber’s age, the yearly expected portfolio return is calculated using the Markowitz standard method, which is provided as

E x p e c t e d p o r t f o l i o r e t u r n = \sum_{i, j = 1}^{M} w_{i} r_{j}

(6)

where

w_{i}

is the weight given at different age under different life cycle strategy and

r_{j}

is the annual return of different asset classes.

Portfolio risk is expressed as the portfolio’s variation in return, which can be written as

σ_{p} = \sum_{i = 1}^{n} \sum_{j = 1}^{m} w_{i} w_{j} σ_{i j}

(7)

where,

σ_{i j}

is the covariance of ith asset with jth asset.

Equally Weighted Strategy

The equally weighted approach (EW), also known as the naive diversification strategy, is a recommended practice of asset allocation. Each asset in this approach is given an equal weighting or $1 / N$ , where $N$ is the total number of asset classes. It is a balanced fund where the risk is uniformly distributed throughout the investment period. According to Benartzi and Thaler (2001), most participants in defined contribution pension plans employ the $1 / N$ rule to allocate their contributions equally among the n alternatives available in their retirement savings plan. Again, (Garlappi et al., 2005) compared the mean-variance (MV) and equally weighted (EW) models. They found that, despite being the most basic form of asset allocation and ignoring the pair-wise correlation between the various assets, the EW portfolio is effective and frequently has a higher Sharpe ratio than portfolios from other static portfolio optimization methods. They concluded that the fundamental EW naive diversification criterion provides a helpful benchmark for assessing the effectiveness of the new asset allocation strategy.

Therefore, the equally weighted strategy has been taken as a benchmark for evaluating other strategies’ effectiveness in this study. As such, the expected portfolio returns and risk using an equally weighted strategy can be computed using equations (6) and (7), respectively.

Genetic Algorithm

A genetic algorithm is a heuristic approach based on genetic principles and Darwin’s theory of evolution’s scientific selection process. John Holland invented it in 1960 and David Goldberg popularized it around 1980 (Fahria & Kustiawan, 2021). This approach manipulates a population of specified size. The population is made up of single points known as chromosomes. This strategy causes chromosomes to compete with one another. Each chromosome encodes a potential answer to the problem to be solved; it is made up of a group of components called genes, each of which can have several values (Abiyev & Menekay, 2007). The population in genetic algorithms undergoes an evolutionary process that comprises mutations (changes in genes in chromosomes), selection (selection of people with the highest fitness value) and crossover (the process of forming new individuals from the results of parent crosses). New individuals produced by the evolutionary process will stand in for the finest candidates for solutions (Fahria & Kustiawan, 2021).

Additionally, the fitness function is constructed, which assesses the population’s chromosomal quality based on the objective function. Generally speaking, the likelihood of keeping a fitness function in the subsequent population increases with its value. A penalty function serving as an optimization restriction might be part of the fitness function (Fahria & Kustiawan, 2021).

Mathematical Formulation of GA Objective Function

In a GA application, evaluation is done using the fitness function, which is established by the given problem and the GA’s optimization goal. The objective is to select the portfolio weights for each asset in order to maximize portfolio return and minimize portfolio risk (Lin & Gen, 2007). Developed by Harry Markowitz, the mean-variance (MV) approach is a fundamental contribution to Modern Portfolio Theory (MPT), and is employed as the objective function for determining optimal portfolio weights in the present study (Markowitz, 1952). According to mean-variance approach, investors are risk averse, which means they choose investments with the highest return for a given level of risk (as measured by the standard deviation) or the lowest risk for a given level of return (Markowitz, 2014). Although other financial ratios such as the Sharpe ratio can evaluate an existing portfolio’s performance, it lacks a systematic approach to portfolio optimization and do not consider diversification’s impact on risk and returns (Sharpe, 1963, 1966). In contrast, the Markowitz mean-variance approach offers a comprehensive framework that explicitly accounts for diversification benefits, enabling investors to construct more efficient portfolios. Moreover, the Markowitz approach can capture complex and non-linear relationships between risk and returns, which the Sharpe ratio, assuming a linear relationship, cannot. This approach has been extensively studied in the field of pension fund’s portfolio optimization over the past several decades (Guambe et al., 2022; Guan & Liang, 2015; He & Liang, 2013; Josa-Fombellida & Rincón-Zapatero, 2008; Kalayci et al., 2017; Liang et al., 2014; Liu et al., 2018; Menoncin & Vigna, 2017, 2020; Yao et al., 2014). Therefore, based on mean-variance theory the total expected portfolio return is presented as

E x p e c t e d p o r t f o l i o r e t u r n (R_{G A}) = \sum_{i, j = 1}^{n} w_{i} r_{j}

(8)

where

w_{i}

is the weight of each asset and

r_{j}

is the annual return of different asset classes.

The maximization of the portfolio return’s objective function may be expressed as follows:

Max {{E x p e c t e d P o r t f o l i o R e t u r n (R}_{G A}) = \sum_{i, j = 1}^{n} w_{i} r_{j}}

(9)

The objective function of the Portfolio variance is presented as

σ_{p} = \sum_{i = 1}^{n} \sum_{j = 1}^{m} w_{i} w_{j} σ_{i j}

(10)

where

σ_{i j}

is the covariance of ith asset with jth asset.

Therefore, the multi-objective function to be maximized can be written as

M a r k o w i t z = R_{G A} - σ_{p}

(11)

Subject to the constraint,

The weights of each asset that make up a portfolio must be equal to 1.

\sum_{i = 1}^{m} w_{i} = 1

(12)

where

i \geq 1,2,3,4, \dots \dots \dots \dots

And

w_{i}^{\min} \leq w_{i} \leq w_{i}^{\max}

(13)

where

w_{i}^{\min}

and

w_{i}^{\max}

are maximum and minimum weight of asset

i

The penalty technique of minimization under constraints has been used for the genetic algorithm application (Abiyev & Menekay, 2007). To ensure that the constraints are adhered to, the penalty function is employed. The restriction states that short selling is not allowed and that the weight must be positive. As a result, the portfolio with the lowest risk will be the one with the global minimum variance. Global minimum variance portfolio size increases with the value of the penalty function. The penalty function is increased by 100 in order to accelerate optimization and attain the global minimum. Since the goal of optimization is to maximize multi-objective function and the penalty function only works for minimizing functions, the Markowitz function is multiplied by −1 (Fahria & Kustiawan, 2021).

Consequently, the fitness function to produce a portfolio with the lowest risk and best portfolio return may be expressed as follows:

F i t n e s s F u n c t i o n = - M a r k o w i t z + 100 [{(\sum_{i = 1}^{N} W_{i} - 1)}^{2} + \sum_{i = 1}^{N} {(\max (0, w_{i} - 1))}^{2} + \sum_{i = 1}^{N} {(\max (0, - w_{i}))}^{2}]

(14)

where penalty function is given as

[{(\sum_{i = 1}^{N} W_{i} - 1)}^{2} + \sum_{i = 1}^{N} {(\max (0, w_{i} - 1))}^{2} + \sum_{i = 1}^{N} {(\max (0, - w_{i}))}^{2}]

(15)

The present study employed a population size of 50, and utilized roulette wheel selection to choose parents based on their fitness values, using a probabilistic method akin to spinning a roulette wheel (Bielecki et al., 2008; Fahria & Kustiawan, 2021; Kalayci et al., 2017; Kantar & Ilhan, 2015; Lin & Gen, 2007). The fittest individuals, one from each of the two selections, were chosen as parents and underwent simulated binary crossover and bit-flip mutation, with a crossover probability of .8 and a mutation probability of .1 (Bartz-Beielstein et al., 2014; Chicano et al., 2015; Forrest, 1996; Immanuel & Chakraborty, 2019). The elitism parameter was set to 2, and the number of generations was fixed at 1000. The termination criteria were defined such that the iterative process ceased when there was no improvement in fitness value for 50 consecutive generations, resulting in the desired return after 462 iterations (Immanuel & Chakraborty, 2019).

Empirical Result

Optimal Asset Allocation-Portfolio Weight

The outcome of the genetic algorithm method provides the following allocation weights: .611731 into equities, .294877 into corporate bonds and .094154 into government bonds. The weight assigned to each asset class under the equally weighted technique is 1/3, or .3333, owing to the study’s use of three different asset classes. Table 4 details the funds using different asset allocation strategies used in the present study.

Table 4.

Asset Allocation Strategies.

Asset Allocation Strategy	Starting Asset Allocation^a	Ending Asset Allocation^a	Glide Path
Aggressive life cycle fund	75/10/15	15/10/75	20 years
Moderate life cycle fund	50/30/20	10/10/80	20 years
Conservative life cycle fund	25/45/30	5/5/90	20 years
Genetic algorithm	61.17/29.48/9.41	61.17/29.48/9.41	—
Equally weighted strategy	33.33/33.33/33.33	33.33/33.33/33.33	—

Source: Authors calculation.

^aShown as a percentage allocated to equity, corporate bond and Government bond respective.

Risk and Return Under Different Life Cycle and Balanced Fund

An essential factor in determining whether weights generated through genetic algorithm is likely to outperform the other is the risk and return attributes of the asset classes chosen for investment. Despite having less equity exposure than the initial equity allocation of the aggressive and moderate life cycle models, equally weighted approach has a greater average expected portfolio return and a lower portfolio standard deviation than all the life cycle models (Table 5). Additionally, the weight of the genetic algorithm produced a significantly higher average expected portfolio return compared to all other strategies with a little higher Portfolio standard deviation than the aggressive life cycle model.

Table 5.

Portfolio Return and Standard Deviation Under Different Life Cycle and Balanced Fund.

Model	Average Expected Portfolio Return	Portfolio Standard Deviation
Aggressive life cycle strategies	.100110	.054913
Moderate life cycle strategies	.094766	.039538
Conservative life cycle strategies	.087455	.022634
Equally weighted strategies	.100319	.039151
Genetic algorithm	.111013	.069317

Source: Authors calculation.

Variability of Monthly Pension and Replacement Rate Under Different Asset Allocation Strategies

Table 6 demonstrates that the weights produced by genetic algorithm give higher replacement rate than the other two asset allocation strategies. The replacement rate under the genetic algorithm is 46.36%, 57.41% and 76.02% which is higher than the replacement rate under aggressive, moderate and conservative life cycle strategies, respectively. The replacement rate under the genetic algorithm is 33.29% greater than the replacement rate under equally weighted strategy. Again, the in-hand accumulation is significantly higher in nominal value using genetic algorithm asset allocation weight than other two strategies.

Table 6.

Expected Monthly Pension and Replacement Rate Under Different Asset Allocation Strategies.

	40% Annuitization	100% Annuitization
Life cycle strategy
Aggressive
In-hand accumulation	$4,23,666.93 (Rs 3,47,78,818.28)	0
Monthly pension	$1,582.06 (Rs 1,29,871.30)	$3,955.14 (Rs 3,24,677.44)
Replacement rate	.292795	.731989
Moderate
In-hand accumulation	$3,93,933.65 (Rs 32338013.32)	0
Monthly pension	$1,471.03 (Rs 1,20,756.85)	$3,677.57 (Rs 3,01,891.72)
Replacement rate	.272247	.680618
Conservative
In-hand accumulation	$3,52,272.39 (Rs 2,89,18,040.49)	0
Monthly pension	$1,315.46 (Rs 1,07,986.11)	$3,288.64 (Rs 2,69,964.45)
Replacement rate	.243455	.608638
Equally weight strategy
In-hand accumulation	$4,65,203.56 (Rs 3,81,88,560.24)	0
Monthly pension	$1,737.16 (Rs 1,42,603.46)	$4,342.91 (Rs 3,56,509.48)
Replacement rate	.321501	.803754
Genetic algorithm
In-hand accumulation	$6,20,097.09 (Rs 5,09,03,770.11)	0
Monthly pension	$2,315.57 (Rs 1,90,085.14)	$5,788.92 (Rs 4,75,212.44)
Replacement rate	.428548	1.071371

Source: Authors calculation.

^a1$ = □82.09 (As of 18/10/2022).

Figure 1 shows the total accumulated wealth at the different age utilizing portfolio return under various asset allocation strategies, assuming a starting age of 25 and an initial salary of $365.45 (Rs 30000) each month, with annual pay growth of nominal 8% and a monthly contribution of 24% of monthly earnings.

Figure 1.

Terminal value of retirement portfolio using different asset allocation strategies. Source: authors calculations.

When compared to other strategies, the genetic algorithm demonstrates the best growth in total accumulated amount. Another significant finding is that an equally weighted asset allocation approach produces more cumulative terminal value than any other life cycle asset allocation method.

Discussion and Conclusion

The goal of a pension plan is to finance the contributor’s post-retirement living expenses. With the increasing adoption of the DC type pension plan, individuals are being called upon to make their own investment decision. Studies have shown that most pension plan subscribers lack financial literacy and also fail to understand the pension plan option given to them. As a result, they either make a wrong decision or choose a default option (life cycle strategy). However, a line of recent studies has shown that the default option leads to sub-optimal retirement wealth and sometimes fails to meet the subscribers’ retirement objective. Therefore, the purpose of the present study was to suggest the optimum asset allocation weight that would maximize the investment outcome of DC pension plan subscribers in India. In this context, the researcher has applied the genetic algorithm to optimize the pension asset of National Pension Fund subscribers in India.

The findings revealed that weights generated by the genetic algorithm are 61.17%, 29.48% and 9.41% in the equity, corporate bond and government bond, respectively. These weights may be used by Indian pension plan subscribers to optimize their retirement amount, as the results of the current study have demonstrated its superiority over other asset allocation weights used in the market. The high equity allocation weight can be justified since India is a developing country and has historically seen very strong returns for stocks, with a 9% equity risk premium over government bonds (Mehra, 2006; Sane & Price, 2018).

Research Implications

The findings indicate significant policy and managerial implications for the NPS subscribers governed by the Pension Fund Regulatory and Development Authority. The revelation that the current default life cycle model may be sub-optimal, despite its intended accommodation of subscribers' limited financial literacy and understanding of pension products, demands a strategic reassessment of the default option.

Considering the magnitude of pension assets and the extensive investment duration, even marginal improvements in investment outcomes can yield significant impacts on subscribers’ well-being during their retirement years. The research highlights the genetically optimized asset allocation weight within a balanced fund as a promising alternative, boasting an average expected portfolio return 1.56% greater than the aggressive life cycle strategy and an impressive 46.36% higher replacement rate.

In light of these compelling findings, policymakers and the PFRDA may initiate a comprehensive review of the default option provided to NPS subscribers. To maximize the impact of these suggestive policy measures, policymakers can adopt the asset allocation weight derived from the genetic algorithm, proven to yield superior investment outcomes.

Furthermore, promoting financial literacy and personalized education is crucial for informed decision-making among NPS subscribers. By providing comprehensive knowledge, tailored guidance and accessible tools, policymakers can empower participants to make wise investment choices aligned with their unique financial goals.

With a strategic focus on optimizing asset allocation, empowering subscribers through financial education and adapting default options to best serve subscribers’ interests, the NPS can set a new standard for pension plan efficiency and subscribers’ long-term financial security.

Limitation of the Study and Scope for Future Studies

Even with the study’s significant contributions, it is crucial to draw attention to the study’s limitations as well, which can be explored in future work. Firstly, many social security institutions have relaxed their investment to other asset class such as infrastructure and REITS the NPS have focussed investment for subscribers only in three asset classes, that is, equity, corporate bond and government bond. Therefore, researchers can also explore the effect of introducing other asset classes that may increase retirement wealth. Secondly, the application of other optimization techniques such as neural network, dynamic programming, simulation optimization, etc. may be explored to optimize the asset allocation weight of pension funds in India. Finally, this study has only considered accumulation phase of National Pension Scheme subscriber. The effect of retirement wealth in the deaccumulation phase has not been explored in India. Thus, the study may also give an interesting conclusion if both the accumulation phase and deaccumulation phase are taken together. Addressing these limitations in future studies will not only refine the findings of this research but also contribute to a more comprehensive understanding of pension fund management and retirement planning in India, fostering more robust and tailored financial strategies for retirees.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Keshav Kant Prasad

Data Availability Statement

The data that support the findings of this study are openly available in NSE website at [https://www.niftyindices.com/reports/historical-data], S&P BSE India Corporate Bond Index at [https://www.spglobal.com/spdji/en/indices/fixed-income/sp-bse-india-corporate-bond-index/#overview] and Government bond data at [].

Appendix

Author Biographies

Keshav Kant Prasad is a Senior Research Fellow at the Department of Management Studies, National Institute of Technology, Durgapur, West Bengal, India. His Research Interest includes Pension Economics and Econometrics.

Dr. Amlan Ghosh is an associate professor at the Department of Management Studies, National Institute of Technology, Durgapur, West Bengal, India. His Research Interest includes Finance, Banking, Pension and Insurance.

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