Modeling and analysis of the effect of COVID-19 on the stock price: V and L-shape recovery
aa r X i v : . [ q -f i n . S T ] N ov Modeling and analysis of the effect of COVID-19 on the stock price: V and L-shaperecovery
Ajit Mahata, Anish Rai and Md Nurujjaman ∗ Department of Physics, National Institute of Technology Sikkim, Sikkim, India-737139.
Om Prakash
Department of Mathematics, National Institute of Technology Sikkim, Sikkim, India-737139. (Dated: November 11, 2020)The emergence of the COVID-19 pandemic, a new and novel risk factor, leads to the stock pricecrash due to the investors’ rapid and synchronous sell-off. However, within a short period, the qualitysectors start recovering from the bottom. A stock price model has been developed to capture theprice dynamics during shock and recovery phases of such crisis. The main variable and parameterof the model are the net-fund-flow ( Ψ t ) due to institutional investors, and financial antifragility ( φ )of a company, respectively. We assume that during the crash, the stock price fall is independent ofthe φ . We study the effects of shock length ( T S ) and φ on the stock price during the crisis periodusing the Ψ t obtained from both the synthetic fund flow data and real fund flow data. We observedthat the possibility of recovery of stock with φ > , termed as quality stock, decreases with anincrease in T S beyond a specific period. A quality stock with higher φ shows V-shape recovery andoutperform others. The T S and recovery period of quality stock are almost equal in the Indianmarket. Financially stressed stocks, i.e., the stocks with φ < , show L-shape recovery duringthe pandemic. The stock data and model analysis show that the investors, in the uncertainty likeCOVID-19, invest in the quality stocks to restructure their portfolio to reduce the risk. The studymay help the investors to make the right investment decision during a crisis. I. INTRODUCTION
The impact of a pandemic on the environment, econ-omy, employment, stock market and many other sectorsis severe [1–4]. A number of pandemics, which hap-pened in − , − and 1968, affectedthe economy and stock markets worldwide badly [5–7].The pandemic’s effect, the coronavirus disease (COVID-19), maybe more severe on the economy and stock mar-ket, including many other sectors, due to its contagionnature [7–9]. The COVID-19 leads to a worldwide stockmarket crash in February and March 2020, created havocamong the investors [10–12]. When economic activitiesthroughout the world were plummeting, surprisingly, inthe stock market, the world witnessed the opposite phe-nomena; the speedy recovery of some stocks and sectorsfrom the crash [10]. These phenomena were also observedduring market crashes in − , 2009 [13]. The studyof market crash dynamics and early recovery of the stocksduring the crisis is fascinating.The stocks with strong fundamentals and positive out-look, which are termed as quality stocks, always showstrength, universality and persistence in returns [14–16].The sustainability and resilience of a quality stock de-pend on its long-term growth prospect and financial abil-ity to fulfill shareholder’s demand [17, 18]. During crises,the unprecedented economic uncertainty forced the in-vestors towards the quality stocks that may be betterable to withstand a downturn, and hence the significant ∗ [email protected] portion of the market capital gets reallocated to thesesectors, which in turn pushes the price up [19]. Thusthe sectors like pharma, healthcare, food, software andtechnology showed the quality of withstanding the down-turn and recovered quickly from the sharp fall. Whereassectors like petroleum, real estate, entertainment, hospi-tality yet to recover because of grim business outlook [10].The quality of a company can be quantified by the fun-damental determinants such as profit over the assets, re-turn on assets, operating cash-flows to total assets, grossmargin, sale growth and some other fundamental deter-minants that assess the reliabilities of profits, low debtand other measures of sustainable earnings [14–16]. In-vestors look for such quality stocks even at a high pre-mium in anticipation of higher returns [14]. The survivaland growth of these quality stocks during pandemic de-pend on the financial antifragility of the company. Finan-cial antifragility is the property that shows the ability ofa company to survive from a financial crisis and performsstrongly after that, and it mainly depends on the finan-cial liquidity position to mitigate the liabilities [20, 21].The stocks with positive antifragility recover very quicklyfrom uncertain shock and survive and sustain for an ex-tended period [20–22].The fund-flow in the market is primarily determinedby the foreign institutional investors (FII) and domesticinstitutional investors (DII). The purchase/sell activityby the FII and DII also influence the retail investors [23].Hence, the net fund-flow by the FII and DII drives thestock price [24–28]. Infusion of a large amount of fund toa particular sector leads to an increase in the stock priceor vice versa, i.e., the price movement is strongly corre-lated with the net fund flow due to FII and DII [27–30].Generally, during a crisis, the FII and DII look for stockswith robust financial antifragility, and hence these stocksbounce back strongly [19]. Hence modeling and analyz-ing stock prices in terms of net fund flow and antifragilityduring shock and recovery phases of a pandemic are es-sential to understanding the market dynamics.Several models describe the stock price movement us-ing various parameters such as return and dividend [31–33]. The efficient market hypothesis (EMH) states thatthe future price does not depend on the past behaviorof data [34]. Contrary to the EMH hypothesis, someother models show that the stock price is partially pre-dictable [35]. However, the stock price prediction remainsa challenging task due to the stock market’s complex na-ture [36]. Recently, a model of V and L shape recovery ofthe economy is proposed in Ref [37, 38] depending on thefragility of the individual firms, where the fragility wastaken as a ration between negative cash balance to thewages. So far, no one has modeled and analyzed stockprices in terms of antifragility and fund flow.The main aim of this paper is to develop a model, andto simulate stock price movement during the COVID-19 shock and subsequent recovery as a function of nor-malized net fund flow ( Ψ t ) due to institutional investorsand the antifragility parameter of a stock. Model simu-lation has been carried out for two different sets of Ψ t :(a) Ψ t obtained from the real fund flow in the market,and (b) artificially generated Ψ t using the distribution ofnet cash flow. Simulation with real fund flow reproducesthe price movement of the quality stocks and financiallystressed stocks during the COVID-19 shock that mimicsthe actual stock price. The model simulation with arti-ficial data shows the effect of various shock-lengths andantifragility parameters. Further, we have analyzed thestock price using EMD based Hilbert Huang transforma-tion in terms of the time scales of the shock and recoveryto identify the quality stocks [39, 40].The rest of the paper is organized as follows: Sec. IIdescribes the formulation of the model. Sec. III discussesthe analysis of the simulated results and original stockprice. Finally, we have concluded the results in Sec. IV. II. MODEL FORMULATION
A model has been developed for the stock price dynam-ics of a stock/sector index during the shock and recoveryperiod. The time steps of the model are discrete with astep of one day. The model’s basic assumptions are thatthe stock price depends on (a) the net fund flow due toFII and DII, and (b) financial antifragility of the com-pany. The basis of the first assumptions is motivated bythe finding of the daily stock return is positively corre-lated with the net fund flow [27, 29, 30]. The retail in-vestors also flock towards the sector in which FII and DIIinvest more. Sometimes the price goes up or down withlag to net fund flow because of information delay [27, 41].Hence, the overall market moves with net fund flow due to institutional investors.During shock, the market falls due to negative senti-ment among the investors, leading to a huge outflow ofcapital from the market. As the pessimism dies down, theinvestors again come to the market, and invest in thosecompanies which have strong fundamentals and positivegrowth prospects. Hence, the fund inflow happens tothe company with positive antifragility [42, 43]. Themodel with the variables normalized-net-fund-flow andantifragility can capture price dynamics very well duringshock and recovery phase.Let us first define the main ingredients of the model.The variable used in the model is the net fund flow, whichcan be calculated as follows. The cash purchase (in-flow) or sell (outflow) by the
F II is denoted as D + F II or D − F II , respectively. Hence, the net cash purchase bythe
F II is D F II = D + F II − D − F II . Similarly, the cash pur-chase (inflow) or sell (outflow) by the
DII is denoted as D + DII or D − DII , respectively. Hence, the net cash pur-chase by the
DII is D DII = D + DII − D − DII . So (the netfund flow due to DII) the net cash purchase is definedas D DII = D + DII − D − DII . Finally, we obtained ∆ D t dueto the purchase or sale by the institutional investors is ∆ D t = D F II + D DII . Finally, we obtained normalized-net-fund-flow, Ψ t = ∆ D t max ( abs (∆ D t )) (1) Ψ t is the variable that is used to update the stock price.The second ingredient of the model is the antifragilityparameter ( φ ), which is estimated as follows: The re-covery of a company after a shock mainly depends oncurrent asset consumed to fulfill the current liabilities ofthe company. The asset that is used, sold, consumed orexhausted during a normal operating cycle is called thecurrent assets of a company. The current assets can easilycover day-to-day financial operations and ongoing oper-ating expenses; hence, it becomes a key component for acompany’s survival or death. The current assets of the i th company, χ i , is defined as χ i = η i + η i + η i + η i , where η i , η i , η i and η i are the current inventories,trade receivables, cash and cash equivalents and othercurrent assets, respectively. Current liabilities are theobligations of a company that consists of short term debtand other similar debts that will be due within a normaloperating cycle. Therefore, we define current liabilitiesof the i th company as ζ i = γ i + γ i + γ i , where γ i , γ i and γ i are the current debt, trade payable and othercurrent liabilities respectively. Hence, the liquidity bal-ance of the company is defined as χ i − ζ i . We characterizethe financial antifragility ( φ ) of the i th company throughliquidity-to-expense ratio φ i = χ i − ζ i ξ i (2)Where ξ i is the operating expenses of a company, andis expressed as ξ i = ϑ i + ϑ i + ϑ i + ϑ i , where ϑ i , ϑ i , ϑ i , and ϑ i are the employment cost, financial cost,maintenance and operating cost and other financial costrespectively. The φ for a sector can be written as φ = P N φ i N (3)Where N is number of company in any sector’s index. φ acts as the control parameter of the price movement.The value of φ > for a quality stock, and φ < for afinancially stressed stock. Usually, φ get updated twicea year based on the financial statement of a company. Itis important to mention that during shock, market nosedives due to massive sell-off by the investors, and hencethe price movement is independent of φ. Our model updates the stock price as a function of Ψ t using the parameter φ as follows P t +1 = P t { λ Ψ t ) } , During shock (4) P t +1 = P t { λ Ψ t φ } , Otherwise (5)Where, λ is the coefficient of Ψ t that represents theproportion of the net fund by the institutional investorsthat flows in a particular company/sector. The valueof λ changes during normal, shock and recovery period.The value of λ has been taken on adhoc basis dependingon the normalized fund flow due to the mutual fund andFPI. Typically the value of λ is in the range of ≤ λ ≤ . There are large numbers of companies and indices inthe stock market. To understand the price movement ofthese companies and indices during the COVID-19 shock,one needs to study the model with different shock andrecovery lengths and antifragility parameters. Hence, inSubsec. II A, the model equations [Eqn 4 and 5] is sim-ulated using artificially generated fund flow data to un-derstand the COVID-like shock. The artificial data isgenerated from the normal distribution of real fund flowduring different phases of the COVID crisis. Further, themodel is studied in Subsec. II B for the COVID-19 shockby using real fund flow and antifragility of the company.
A. COVID-like shock
Study of the effect of the COVID-like shock on thestock prices in terms of various shock lengths ( T S ) anddifferent φ is very important to understand the marketcrash and subsequent recovery. We have generated syn-thetic normalized fund flow ( Ψ st ) data from the distribu-tion of Ψ t [Eqn. 1] during the normal, shock and recov-ery period. The distribution of Ψ t for the normal, shockand recovery periods are N (0 , . , N ( − . , . and N (0 . , . , respectively, and accordingly Ψ st is gener-ated. As the distribution of the Ψ t is derived from realdata, the Ψ st mimics the real situation. In this modelsimulation, the recovery time period ( T R ) is taken equalto T S , and the justification is given in detail in Sub-sec. III C. The value of λ = 0 . , . , . , . during pre-covid normal period, shock period, recovery periodand post recovery period, respectively. The reason forchoosing different values of λ during different periods isdiscussed in Sec.II B.To understand the V-shape recovery of a quality stock,the model simulation is carried out for the fixed φ = 0 . with T S = 20 day ( D ) , D, D, and D , respec-tively, and for the fixed T S = 20 D with φ = 0 . , . , . and . . The value of φ and T S are chosen based onthe original stock price. Similarly, for the L-shape re-covery of the financially stressed company, simulation iscarried for the φ = − . with T S = 20 D, D, D, and D , respectively, and for the T S = 20 D with φ = − . , − . , − . and − . . In this case, thevalue of φ and T S are chosen on the basis of the originalstock price. The detailed simulation result is given inSec. III. B. COVID-19 shock
The model simulation has been carried out for thestock price during the COVID-19 using the Ψ t and φ for the Indian market. The Ψ t has been calculated fromreal net fund flow in the market due to FII and DII usingEqn. 1. The fund flow data has been obtained from themoney control website [44]. The current financial statusof a company, φ , is estimated using Eqn. 2. The value of φ for a sector has been calculated using Eqn. 3. The cur-rent assets, current liabilities and expenses of a companyhave been derived from its financial statements, which areobtained from Bombay Stock Exchange Ltd (BSE) [45].The coefficient λ for a particular stock depends on theratio of fund flow to total fund flow in the market. Inthe present case, the value of λ is taken in adhoc man-ner that can be guessed from the fund flow to a sectordue to the institutional investors. Fig. 1(a) shows thenormalized monthly fund flow due to mutual fund in-vestors (MFI) in Pharma & Biotechnology ( − ∗ − PH),Fast Moving Consumers good( −∇−
FMCG) and HotelRestaurant and tourism( − ⋄ −
HRT). The above sectordata has been obtained from the Securities and ExchangeBoard of India (SEBI) [46]. Fig. 1(b) shows the nor-malized fortnightly fund flow due to foreign portfolio in-vestors (FPI) in Pharma & Biotechnology ( − ∗ −
PH),Fast Moving Consumers good( −∇−
FMCG) and HotelRestaurant and tourism( − ⋄ −
HRT), and the data hasbeen obtained from National Securities Depository Ltd.,India (NSDL) [47]. The figure shows that the fundflow during shock decreased significantly, and during therecovery phase, fund flow in the pharma and FMCGsectors increased significantly. On the other hand, inthe Hotel Restaurant and tourism sector, fund flow re-mains almost constant after a drastic drop. Consider-ing the above information, for the quality stock, we havetaken λ = 0 . , . , . , . for Nifty Pharma and λ =0 . , , . , . for Nifty FMCG index during the pre-COVID normal period, shock period, recovery period and
31 Jan 31 Mar 31 May 31 Jul
Time (monthly) N o r m a li s e d F und f l o w PHFMCGHRT
31 Jan 31 Mar 31 May 31 Jul
Time (fortnightly) N o r m a li s e d F und f l o w PHFMCGHRT (b)(a)
FIG. 1. Plot (a) shows the monthly data of the normalizedfund flow due to mutual fund in Pharma ( − ∗ −
P H ), FMCG( −∇ −
F MCG ) and Hotel and Tourism ( − ⋄ −
HRT ) sectors.Plot (b) shows the fortnightly data of the normalized fundflow due to FPI in Pharma ( −∗−
P H ), FMCG ( −∇−
F MCG )and Hotel and Tourism ( − ⋄ −
HRT ) sectors. post-recovery period, respectively, and for a financiallystressed stock, like Tata Motors, λ = 0 . , . , . , . and for BPCL λ = 0 . , . , . , . during the abovefour periods. The detailed simulation result is given inSec. III. III. RESULTS AND DISCUSSION
This section aims to present the simulation results ofthe effect of the T S and φ on the V- and L-shape recoveryof the stock price. The analysis of the original price andthe simulated price has also been carried out to identifythe shock and recovery time scales of the stock price. A. Simulation of COVID-like shock
Fig. 2(a) shows the typical plot of V-shape recovery ofa quality stock using Ψ st for different T S with φ = 0 . . As the typical value of φ for a quality sector is around0.4. The plot − , −− , · · · , and − · − show the stock pricemovement for the T S = 20 D, D, D, and D , re- P r i ce s =20 D s =40 D s =60 D s =80 D Time (day) P r i ce =0.3=0.4=0.5=0.6 (a)(b) FIG. 2. Plot (a) shows the V-shape recovery using the syn-thetic data for fixed φ = 0 . with T S = 20 D, D, D and D . Plot (b) shows the V-shape recovery using syn-thetic data for fixed T S = 20 D with φ = 0 . , . , . and0.6. D and φ represent day and financial antifragility. Verti-cal dashed line represents the starting point of shock. For thesimulation initial condition is taken as 0.5 spectively. The results show that the quality stock recov-ers very well to its pre-shock price for the T S = 20 D and D . However, when the shock extended beyond D ,it becomes difficult to recover because of the stock price’sserious crash. It implies that the extended period of T S isharmful even for the financially strong company. Duringsuch kind of extended shock, the investor stays away frominvestment in the market, which is sometimes termed bythe investors "Do not catch a falling knife" [48].Fig. 2(b) shows the typical plot of V-shape recovery ofquality stocks for different φ with T S = 20 D. The typicalvalue of T S was 20 D during the COVID-19 for a qualitysector. The plot − , −− , · · · , and − · − show the stockprice movement for the φ = 0 . , . , . and . , respec-tively. The higher the value of φ , the recovery is rapid.The results show that the quality stock recovers very wellfor positive φ . Further, the quality stocks with higher φ outperform its peer. Hence, the financially strong com-pany recover from the shock and outperform compared toanother company observed during the COVID-19 [42, 43].During crises, the investors invest heavily in such com-panies, and hence generates higher return [49].Fig. 3(a) shows the typical plot of L-shape recovery of afinancially stressed stock for different T S with φ = − . . Typical value of φ for this sector is around − . . Theplot − , −− , · · · , and −·− show the stock price movementfor the T S = 20 D, D, D, and D respectively.The simulation results show that the financially stressedstock does not recover. As the value of T S increases,the negative depth of stock price also increases. So, afinancially stressed company cannot survive the extended T S , and have a big chance to die down. The investorsbecome very bearish on these company, and sell-off theirpositions, and hence the chance of the recovery of thestock price also becomes marginal.Fig. 3(b) also shows the typical plot of the L-shapebehavior of a financially fragile stock for different φ with T S = 20 D. The plot − , −− , · · · , and −·− show the stockprice movement for the φ = − . , − . , − . and − . , respectively. For the simulation of COVID-likeshock we have taken 0.5 as initial condition. The com-pany with negative φ continues to slide down even duringthe recovery phase of the overall market. The lower the φ , the slide in stock price is rapid. So, a company witha lower φ has a big chance to die down. As the investorsstay away from these companies, the chance of the stockprice recovery also becomes marginal as mentioned in theprevious paragraph. B. COVID-19 shock
Fig. 4(a) and 4(b) show the simulation result ( −− )of the model using the normalized fund flow Ψ t givenin Eqn 1, and − represents stock price of the Pharmaand FMCG index in Indian market during the COVID-19 shock. The simulation results of Pharma and FMCGindices show that the fall of the stock price due to theCOVID-19 shock starts from st week of March 2020, andforms a bottom on th week of April 2020, as shown inFig. 4(a) and 4(b), respectively. The model simulationshows a V-shape recovery in the stock price consistentwith the original stock price during the shock, as shownin the same figure. We observed a lag in the formation ofthe bottom between the model simulation data (SD) andoriginal data (OD). Original stock price recovers earlierthan the model. The possible reason for such lag maybe due to the fund allocation in the quality sectors bythe investors internally, which was not reflected in thefund flow. For example, in India, during the pandemic,the outlook in the Pharma and FMCG sectors becomespositive, hence the fund allocation to these sectors dueto DII and retail investors increased rapidly that can beunderstood only from investors’ buying sentiment. Themodel for the quality index and company may behaveproperly with minimum lag if index or company wise fundflow data were available.Fig. 5(a) and 5(b) show the simulation result for thestock price that show L-shape recovery in Indian marketduring COVID-19 shock. The simulation for Tata Motorsand BPCL show that the fall of the stock price due tothe COVID-19 shock starts from st week of March 2020,and forms a bottom on th week of March 2020 as shownin Fig. 5(a) and 5(b), respectively. We observed that P r i ce s =20 D s =40 D s =60 D s =80 D Time (day) P r i ce =-0.05=-0.15=-0.25=-0.35 (a)(b) FIG. 3. Plot (a) shows the L-shape recovery using the syn-thetic data for fixed φ = − . with T S = 20 D, D, D and D . Plot (b) shows the L-shape recovery using the syn-thetic data for fixed T S = 20 D with φ = − . , − . , − . and -0.35. For the simulation initial condition is taken as 0.5. D and φ represent day and financial antifragility. the stock with φ < does not recover from the bottom,i.e., the behavior of the price is L-shape, as shown in thesame figure. The main reasons for the poor allocationof the fund, as shown in Fig. 1 in these stressed stocks,are the non-essential nature of the product they produce,negative outlook during COVID-19. C. Time scale Analysis
The empirical mode decomposition (EMD) techniqueis applied to identify the important T S and T R of stocksand indices during the COVID-19 [50, 51]. The EMDtechnique decomposes a signal into a number of intrinsicmode functions (IMF) of different time scales by pre-serving the nonlinearity and nonstationarity of a timeseries [52]. The detailed algorithms for identifying theIMF using the EMD method is given in Ref. [40, 50].The range of a time period of a particular IMF canbe obtained using τ = 1 ω , where ω = dθ ( t ) dt . The ω of a particular IM F can be estimated by using HilbertTransform, which is defined as Y ( t ) = Pπ Z ∞−∞ IM F ( t ) t − t ′ dt, P r i ce OD SD
14 Jan 13 Apr 8 Jul
Time (day) P r i ce OD SD (b)(a)
FIG. 4. Plot (a) represents the original stock price movementof Nifty Pharma ( − OD ) and its corresponding model sim-ulated stock price movement ( − − SD ) with φ = 0 . and T S = 20 D . Plot (b) represents the original stock price move-ment of Nifty FMCG ( − OD ) and its corresponding modelsimulated stock price movement ( − − SD ) with φ = 0 . and T S = 20 D P r i ce ODSD
Time (day) P r i ce ODSD (a)(b)
FIG. 5. Plot (a) shows the original stock price movement ofTata Motors Ltd ( − OD ) and its corresponding model simu-lated stock price movement ( − − SD ) with φ = − . and T S = 20 D . Similarly, plot (b) shows the original stock pricemovement of BPCL ( − OD ) and its corresponding model sim-ulated stock price movement ( − − SD ) with φ = − . and T S = 20 D . OD -2000200 I M F -2000200 I M F -7000700 I M F -5000500 I M F Time (day) R e s i du e FIG. 6. Original data (OD) of Nifty Pharma and its IMF andresidue obtained using empirical mode decomposition (EMD)technique. where P is the Cauchy principle value, and θ ( t ) = tan − Y ( t ) IM F ( t ) [50]. We have applied EMD based HilbertHuang Transformation to obtain the τ of the stock data.We have identified the τ of the Nifty Pharma and NiftyFMCG index as quality stocks, and their model simulateddata during the COVID-19 shock. The data were takenfrom [53, 54].Fig. 6 shows the IMF of the Nifty Pharma index esti-mated using the EMD technique. The series is decom-posed into four IMFs and a residue. Fig. 6 shows thevisualization. IMF1 represents the signal with the lowest τ , and the τ increases with the increase in IMF numbers.The residue represents the overall long-term trend of theindex. Each IMF represents a mono-frequency compo-nent of the stock data.In order to identify the τ of the COVID-19 shock andsubsequent recovery of the quality stocks, we have firstidentified the dominant IMF that fits the event as fol-lows. We have calculated the correlation coefficient ( ν )between the original stock price and its IMFs and model-simulated stock price and its IMFs. We have also cal-culated variance ( σ ) of the IMFs as shown in Table I.The value of ν measures the relationship between the in-dividual IMF and the stock price. Whereas, the valueof σ measures the volatility of each IMF. From the Ta-ble I, the values of ν and σ shows that the IMF4 is thedominant mode for the original pharma and FMCG in-dex and their model simulated data. All the four IMF4modes along with their time series are shown in Fig 7 (a),(b) (c) and (d), respectively. The average τ of the IMF4 TABLE I. Measures of correlation coefficient ( ν ) between original data (OD) and its IMFs and model simulated data (SD) andits IMFs of NIfty Pharma and Nifty FMCG index. Variance ( σ ) has been calculated for the IMFs of OD and SD.IMF NO. Nifty Pharma index Nifty FMCG indexOD SD OD SD ν σ ν σ ν σ ν σ IMF1 0.1456 8.81 × × . × × IMF2 0.0576 1.75 × . × × × IMF3 0.4219 2.44 × × × × IMF4 0.7394 1.76 × × × × for the pharma, FMCG index and simulated pharma andFMCG are approximately 57 D , 56 D , 58 D and 58 D ,respectively. Vertical lines in the figure show the bottomformation due to the COVID-19 shock. All the IMF4shows that T S and T R are almost equal. For the pharmaand FMCG stocks T S ≈ T R ≈ D. We have obtainedthat the T S ≈ T R for all the quality stocks that show V-shape recovery. It is pertinent to mention that there is nodominant mode present in the case of L-shape recovery. IV. CONCLUSION
In this paper, we have developed a model of the stockprice movement during the COVID-19 shock and its sub-sequent recovery. The simulation is carried out assum-ing that during shock, the price crashes due to the fundoutflow from the market, and does not depends on thefinancial antifragility ( φ ) of a company. Whereas, therecovery of the stock price depends on the fund inflowtowards a particular company or sector depending on φ .The model simulates the stock price for different T S anddifferent φ using synthetic normalized net fund flow. Themodel reproduces the stock price movement during thepandemic very well. We have also identified the T S and T R from the model and original data using EMD basedHilbert Huang Transformation.We obtained V-shape recovery of the quality stockswith positive φ using synthetic normalized net fund flow( Ψ st ). The stock price recovers very well to its pre-shockvalue for the T S = 20 D and 40 D with fixed φ = 0 . .However, when the T S extends beyond 60 D, it becomesdifficult for the stock price to recover to its pre-shockprice. We also obtained the V-shape recovery for φ = 0 . , . , . and 0.6 with fixed T S = 20 D . The stockwith a higher φ outperforms its peer with a lower φ aftercrises. Such performance in the stock price of certainquality stocks have been observed during the COVID-19pandemic. In the case of the financially stressed stocks,i.e., with negative φ , we obtained L-shape recovery of thestock price, and such stocks show higher negative depthin stock price with an increase in T S . As the value of φ decreases, the duration of T S increases that have beenobserved in several stocks during the pandemic.We obtained V-shape recovery from the model usingthe normalized net fund flow Ψ t . In this simulation, wehave used the average value of φ of the Pharma andFMCG. The simulated results are consistent with theoriginal stock price movement of the Pharma and FMCGindices during the COVID-19 shock. On the other hand,for the companies with negative φ , the model also con-sistent with L-shape movement of price.Finally, we obtained that the T S and T R of a qualitystock during the COVID-19 is approximately equal. Onthe other hand, the companies with φ < is yet to re-cover. The value of T S and T R for different sectors will beuseful for making an investment decision. We observedthat for some sectors like the banking where φ > , itstill shows L-shape recovery. Such recovery depends onvarious other factors which will be studied in future work. ACKNOWLEDGMENTS
The authors acknowledge Jean-Philippe Bouchaud,Dhurv Sharma and Paresh K. Narayan for their valuablecomments and suggestions to improve the manuscript.NIT Sikkim is appreciated for allocating doctoral re-search fellowships to A.M. and A.R. [1] S. Muhammad, X. Long, and M. Salman, Science of TheTotal Environment, 138820(2020)[2] R. J. Barro, J. F. Ursúa, and J. Weng,
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10 Feb 11 Mar 13 Apr 13 MayTime (day)220002400026000280003000032000 P r i ce -2000-10000100020003000 I M F ODIMF4
25 Feb 25 Mar 28 Apr 28 MayTime (day)220002400026000280003000032000 P r i ce -2000-10000100020003000 I M F SDIMF4 (c)(a) (b)(d)
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