Valuation in the Life Settlements Market

Transcription

1 Valuation in the Life Settlements Market New Empirical Evidence Jiahua (Java) Xu 1 1 Institute of Insurance Economics University of St.Gallen Western Risk and Insurance Association 2018 Annual Meeting Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

2 Agenda 1 Motivation of the study 2 Methodology 3 Empirical analysis 4 Interpretations of the findings Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

3 Motivation of the study The study is conducted to fulfill multiple objectives The research objectives listed below are tightly connected and not mutually exclusive: To comply with regulations Several regulations require assets to be held at fair value International Financial Reporting Standards (IFRS) 13 Alternative Investment Fund managers Directive (AIFMD) To provide guidance for life settlement bidders The two-variable model developed in the study can be used as a valuation rule of thumb. To raise the awareness of the importance of LE accuracy LE is the driver of life settlement valuation. Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

4 Motivation of the study Life expectancy is the key driver of price theoretical evidence 80-Year-Old Male Non-smoker P0 Simulated P0 IRR k-relationship k = 3.0 or LE = 7.8 k = 1.5 or LE = 10.4 k = 1.0 or LE = P0 = 0.2 P i= k, or its natural logarithm ln k, is used to indicate underwriting aggressiveness, throughout the study IRR πi Probi IRR i + P i=1 1 Probi IRR i, where TP P0 = : transaction price (TP) as a fraction of death benefit () k: implied mortality multiplier (VBT 2015) LE : life expectancy (in years) Probi : Survival probability at time i πi : premium rate (to ) at time i k up Probi down & LE down & P0 up Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

5 Agenda 1 Motivation of the study 2 Methodology 3 Empirical analysis 4 Interpretations of the findings Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

6 Methodology Dependent variables Two variables to proxy valuation: TP : Price multiplier; Transaction price TP as a fraction of death benefit - We bought the policy at 20 cents on the dollar - cash-flow-based - more direct, less comparable RP: Risk premium; internal rate of return IRR in excess of risk-free rate r - This policy was sold at 20% - return-based - less direct, more comparable Relation of the two: TP = f (RP) = C i (1 + RP + r) i, i=0 Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

7 Methodology Independent variables Log-linear best describes LE- TP relationship: T P = LE R 2 = LE Figure: Linear T P LE Figure: Log-linear = ln LE R 2 = T P = LE LE LE 3 R 2 = LE Figure: Polynomial T P = exp( LE) R 2 = LE Figure: Exponential Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

8 Risk proxies I Independent variables Variables that affect both valuation proxies: risk risk up TP down; RP up Longevity risk Stemming from inaccurate (or most likely too short) LE estimates ln LE Natural logarithm of life expectancy ln Natural logarithm of death benefit DI Difference in LE estimates MK Market NO Number of LE estimates AG Insured s age CO Premium convexity Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

9 Risk proxies II Independent variables Premium risk Pertaining to an increase in premiums of an in-force policy PM Sum of expected premiums as a fraction of death benefit Default risk Linked to the uncertainty in insurers ability to honor claims should financial distress occur RT Credit rating Rescission risk Associated with insurance carriers refusal to pay the death benefit due to a lack of insurable interest or other fraudulent behavior at issue VI Vintage Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

10 Agenda 1 Motivation of the study 2 Methodology 3 Empirical analysis 4 Interpretations of the findings Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

11 Descriptive statistics Full sample divided into in-sample and out-of-sample data n Min Median Max µ σ γ κ Full sample (01/07/ /31/2016) TP (kusd) 2, , PM (kusd) 2, , CS (kusd) 2, , (kusd) 2, , , , , LE (year) 2, AG (year) 2, VI (year) 2, k ( ) 2, , RP (%) 2, TP (%) 2, PM (%) 2, CS (%) 2, In-sample (01/07/ /14/2015): 2/3 of full sample for model training Out-of-sample (10/14/ /31/2016): 1/3 of full sample for backtesting Statistical similarity between the in-sample and the out-of-sample data legitimizes modelling policy values empirically Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

12 Regression modelling A two-variable linear model is most efficient for TP Standardized coefficient *** *** *** *** *** ** *** * *** * 1, , *** *** *** *** *** ** *** * * *** 1, , *** *** *** *** *** ** *** * *** 1, , *** *** *** *** *** *** *** * *** 1, , *** *** *** *** ** *** *** *** 1, , *** *** *** *** *** *** *** 1, , *** *** *** *** *** *** 1, , *** *** *** *** *** 1, , *** *** *** *** 1, , *** *** *** 1, , *** *** 1, ,044 df RMSE R 2 Radj 2 BIC Number of variables c ln LE ln RMSE P M DI RT MK P T R 2 NO AG V I CO Number of variables Model selected: P M = ln LE R 2 adj BIC Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

13 Regression modelling A three-variable linear model is most efficient for RP Standardized coefficient ** *** *** *** * *** * *** *** *** * *** ** *** *** *** * *** ** *** *** *** * * *** ** *** *** *** * *** * *** *** *** * *** *** *** *** ** *** *** *** *** *** *** *** *** *** *** *** *** Number of variables c ln LE ln RMSE P M DI RT MK P T R 2 NO AG *** 0.07 *** 0.07 *** 0.07 *** 0.07 *** 0.07 ** 0.07 ** 0.07 ** V I CO 1,710 1,810 1,811 1,812 1,813 1,814 1,815 1,816 1,905 1,906 1, df RMSE R R 2 adj BIC Model selected: RP = ln LE ln P M R 2 adj Number of variables BIC Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

14 Model performance TP well modelled, RP not TP estimated with regression result for TP good performance in in-sample estimation & out-of sample prediction RP estimated with regression result for RP poor performance in in-sample estimation & out-of sample prediction T P NULL RP NULL In-sample (01/07/ /14/2015) P M = ln LE < T P > T P 95%-CI 95%-PI n = 1, 909 ME = MAE = RMSE = R 2 = In-sample (01/07/ /14/2015) RP = ln LE ln P M RP < RP RP > RP n = 1, 909 ME = MAE = RMSE = R 2 = Index RP NULL NULL 95%-CI 95%-PI Out-of-sample (10/14/ /31/2016) P M = ln LE < T P > T P 95%-CI 95%-PI n = 954 ME = MAE = RMSE = R 2 = Index Out-of-sample (10/14/ /31/2016) RP = ln LE ln P M RP < RP RP > RP 95%-CI 95%-PI n = 954 ME = MAE = RMSE = R 2 = Index Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

15 Model performance More efficient and effective to model TP directly TP estimated with regression result for TP good performance in in-sample estimation & out-of sample prediction TP = f ( RP), RP estimated with regression result for RP worse performance in in-sample estimation & out-of sample prediction T P NULL T P NULL In-sample (01/07/ /14/2015) P M = ln LE < T P > T P 95%-CI 95%-PI n = 1, 909 ME = MAE = RMSE = R 2 = In-sample (01/07/ /14/2015) RP = ln LE ln P M < T P > T P n = 1, 909 ME = MAE = RMSE = R 2 = Index = f( RP ) NULL NULL Out-of-sample (10/14/ /31/2016) P M = ln LE < T P > T P 95%-CI 95%-PI n = 954 ME = MAE = RMSE = R 2 = Index Out-of-sample (10/14/ /31/2016) RP = ln LE ln P M < T P > T P n = 954 ME = MAE = RMSE = R 2 = Index Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

16 Model performance TP can be well described simply through LE and premiums TP estimated with regression result for TP good performance in in-sample estimation & out-of sample prediction T P NULL In-sample (01/07/ /14/2015) P M = ln LE < T P > T P 95%-CI 95%-PI n = 1, 909 ME = MAE = RMSE = R 2 = NULL Out-of-sample (10/14/ /31/2016) P M = ln LE < T P > T P 95%-CI 95%-PI n = 954 ME = MAE = RMSE = R 2 = Index TP = f ( RP) = f (0.214), as mean RP from in-sample data worse performance in in-sample estimation, better in out-of sample prediction T P NULL In-sample (01/07/ /14/2015) RP = < T P > T P n = 1, 909 ME = MAE = RMSE = R 2 = Index = f( RP ) NULL Out-of-sample (10/14/ /31/2016) RP = < T P > T P n = 954 ME = MAE = RMSE = R 2 = Index Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

17 Robustness test Robustness test of different policy types Policy type Universal life Term life Whole life Coeff. p sig. Coeff. p sig. Coeff. p sig. c *** *** *** ln LE *** *** *** PM *** *** *** BP test *** In-s. In-s. Performance In-s. Outof-s. Outof-s. Outof-s. n 1, ME MAE RMSE R Disregarding policy type Whole life which contains very few observations, the model stays robust. Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

18 Robustness test Robustness test of different rating classes Rating A-rated B-rated No rating Coeff. p sig. Coeff. p sig. Coeff. p sig. c *** *** *** ln LE *** *** *** PM *** ** BP test *** In-s. In-s. Performance In-s. Outof-s. Outof-s. Outof-s. n 1, ME MAE RMSE R Disregarding rating class No rating which contains very few observations, the model stays robust. Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

19 Agenda 1 Motivation of the study 2 Methodology 3 Empirical analysis 4 Interpretations of the findings Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

20 Interpretations of the findings Why RP can hardly be modelled Risk behavior: - policy purchases do not reflect a significant level of risk-aversion Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

21 Interpretations of the findings Why RP can hardly be modelled Risk behavior: - policy purchases do not reflect a significant level of risk-aversion Risk premium proxy: - applied vs. implied risk premiums Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

22 Interpretations of the findings Why RP can hardly be modelled Risk behavior: - policy purchases do not reflect a significant level of risk-aversion Risk premium proxy: - applied vs. implied risk premiums inherent property of IRR: - non-injectivity on return to price (multiroot) - decresing elasticity of price on return Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21

23 Thank you! Contact Jiahua (Java) Xu Institute of Insurance Economics, University of St.Gallen I.VW-HSG Tannenstrasse 19, 9000 St.Gallen, Switzerland T: M: Xu (I.VW-HSG) Valuation in U.S. Life Settlements / 21