How Insolvent Are We

7/30/2019 How Insolvent Are We

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H O W I N S O L V E N T A R E W E ?P . D . J O H N S O N

C a n a r c h a eo l o g y h e lp u s ?A s w e g r a p p l e w i t h t h e p r o b l e m s o f c o n d u c t i n g n o n -l if e in s u r a n c e

i n a w o r l d o f h i g h i n fl a ti o n , w e s h o u l d p e r h a p s p a u s e f o r a m o m e n tt o l o o k f o r h i s t o r ic a l a n a l o g i e s f o r o u r p r e s e n t p r e d i c a m e n t . L e t u s,t h e n , l o o k b a c k a t a d i s tr e s s in g p e r i o d m a n y y e a r s a g o i n t h eh i s to r y o f t h e K i n g d o m o f C a r m a n i a .

I n f l a t io n w a s b y n o m e a n s n e w t o t h e c i ti ze n s o f C a r m a n i a .Y e a r a f t e r y e a r , a l l p r i c e s a n d i n c o m e s h a d b e e n r i s i n g a t a s t e a d yr a t e o f 5 % p e r a n n u m . T h e e c o n o m y f u n c t io n e d q u i t e w e ll , a lb e i ti n a r a t h e r u n i n t e r e s t i n g w a y , a n d t h e p e o p l e w e r e a c c u s t o m e d t ot h e id e a t h a t t h e p u r c h a s i n g p o w e r o f t h e C a r m a n i a n d o l la r w o u l df al l b y r o u g h l y 5 % e v e r y y e a r. T h e r e w e r e , h o w e v e r , s o m e e c o n o -m i s t s w h o a r g u e d t h a t i n f la t io n w a s b o t h u n d e s i r a b l e a n d u n -n e c e s sa r y , a n d p r e v a i l e d u p o n t h e K i n g t o a d o p t s o m e m e a s u r e sw h i c h , t h e y a s s u r e d h i m , w o u l d q u i c k l y r e d u c e t h e r a t e o f i n f la t io nt o ze ro . T h e m e a s u r e s w e r e a d o p t e d , a n d t h e f o ll ow i n g y e a r t h er a t e o f i n f l a ti o n r o s e t o l O % .

A t t h is p o i n t a r iv a l g r o u p o f e c o n o m i s ts e x p l a i n e d t h a t t h isu n f o r t u n a t e d e v e l o p m e n t w a s s i m p l y w h a t s h o u ld h a v e b e e ne x p e c t e d , a n d t h e y s e t o u t a n a l t e r n a t i v e p o l i c y w h i c h w o u l du n d o u b t e d l y r e v e rs e t h e t r e n d a n d b r in g i n f la t i o n q u i c k ly u n d e rc o n t r o l. C o n v i n c e d b y t h e w e i g h t o f t h e i r a r g u m e n t s , t h e K i n gi n t r o d u c e d w h a t b e c a m e k n o w n a s P h a s e 2 o f t h e c o u n t e r -i n f l a t i o np o l ic y . B y t h e n e x t y e a r , t h e r a t e o f i n fl a ti o n h a d r i se n t o 2 0 % .

H e r e u p o n a th i r d g r o u p o f e c o n o m i s t s , w h o h a d b e e n t r a v e l l i n gt o m a n y f o re i gn la n d s , r e t u r n e d w i t h n e w s o f h o w , in o n e of t h o s ec o u n t r ie s , t h e r a t e o f i n f la t io n h a d b e e n b r o u g h t d o w n f r o m n ole ss t h a n 8 o % t o I o % b y a d o p t i n g p o li ci es w h o s e w i s d o m w a s s oo b v i o u s t h a t i t r e q u i r e d - - a n d r e c e i v e d - - n o e x p la n a t i o n . W i t hg r e a t 1 7e lie f, t h e K i n g s e i z e d u p o n t h e s e n e w p o l ic i e s , c a ll e d t h e mP h a s e 3 a n d p u t t h e m i n t o f o rc e . T h e r a t e o f i n f la t io n r o s e t o 3 o % .

B y t h is ti m e , t h e K i n g w a s b e g i n n i n g t o w o n d e r w h e t h e r h i s


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1.40 IIOW INSOLVENT ARE WE )

faith in economists was entirelv justified. After giving the mattercareful thought, he decided to dismiss all his economists and adoptsome new measures which were entirely his own.

While all this was going on, the members of the CarmanianInsurance Association (CIA) were naturally experiencing somedifficulties. The extent of these can be gauged from the historicalrecords, discovered during recent excavations, for one companywhose business consisted entirely of chariot insurance.

During the long period of 5~/o inflation, the company's businessshowed a remarkable stability. Not only did the volume of businessremain constant but the expenses and the pattern of claim pay-ments remained unchanged apart from the regular increase of 5%over the amounts for the previous year. Every claim payment wasmade on 3Ist December and, expressed in terms of the purchasingpower of a base year, the pattern of payments for each year'sclaims was as foUows, where yea r C is the yea r of claim :

Year C C+ t C+2 C + 3 C + 4 C + 5 C + 6Pa ym en ts at end of 3"ear 55 -'40 80 60 3 20 2oCumula ti ve pa ym en ts 55o 79o 87o 93 96o 98o IOOOThe actual payments made at the various durations, and the

cumulative payments, would be equal to the value of the inflationindex for the end of,the year of claim, multiplied by the followinga m o u n t s :

Year C C+ t C-+-2 C4-3 C 4 C+ 5 C+ 6Pa ymen ts at end o[ yea r 550 252 88 69 36 26 27Cumula tive pa ym en ts 550 802 890 959 995 xo2I lO48Expenses associated with the settlement of claims are included

in the above payments. Other expenses, amouting to 300, wereall paid at the end of the year of claim. In addition, commissionwas paid at the rate of 157/0 of the premiums, which were all dueon ISt January.Y ear o : t he l a s t year o f t ranqu i l l i t y

We shall begin our story in year o, the last of the long series ofyears with inflation at 5,/o. The value of the inflation index at theend of year o was unity.

All money was placed on short-term deposit and earned a rate


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HOW INSOLVENT ARE WE ? I 4 1

o f i n t e r e s t o f 5 % , t h e s a m e a s t h e r a t e o f in f la t io n . T h e p r e m i u m so f x 45 6 c h a r g e d o n I s t J a n u a r y o f y e a r o , a f t e r d e d u c t i o n o f c o m -m i s s io n a m o u n t i n g t o 2 1 8 , e a r n e d i n t e r e st o f 6 2 a n d w e r e t h e r e f o r ej u s t s u f f i c i e n t t o m e e t t h e t o t a l c l a i m a n d e x p e n s e p a y m e n t s o fI 3 o o a t t h e e n d o f t h e y e a r . A t t h e s t a r t o f t h e y e a r t h e p r o v i s i o nf o r o u t s t a n d i n g c l ai m s w a s 8 7 6 a n d t h e f re e r e s e rv e s a m o u n t e d t oI 4 56 , e x a c t l y i o o % o f t h e p r e m i u m s p a i d on I s t J a n u a r y . O f t h et o t a l f r e e r e s e r v e s o f I 4 5 6 , 5 o o r e p r e s e n t e d s h a r e h o l d e r s ' c a p i t a l .I n t e r e s t a t 5 % o n t h e p r o v i si o n f o r o u t s t a n d i n g c l ai m s a n d o n t h a tp a r t o f t h e f r e e r e s e r v e s w h i c h d i d n o t r e p r e s e n t s h a r e h o l d e r s 'c a p i t a l w a s e x a c t l y s u ff i c ie n t to m a i n t a i n t h e i r r ea l v a lu e , a n d t h u sa t t h e e n d o f t h e y e a r t h e y s t o o d a t 9 2 o a n d I o o 4 T e s p e c t iv e l y .T h e s h a r e h o l d e r s r e c e i v e d d i v i d e n d s a t t h e r a te o f 5 % a n d , f o rr e a s o n s w h i c h h a v e n o t b e e n d i s c o v e r e d , w e r e a p p a r e n t l y q u i t ec o n t e n t t o r e c e i v e a r e t u r n n o g r e a t e r t h a n t h a t w h i c h t h e y c o u l dh a v e o b t a i n e d b y s i m p l y p l a c in g t h e ir m o n e y o n d e p o s it . A t a n yr a t e , t h e c o m p a n y h a d n o d i f f ic u l t y i n f in d i n g p e o p l e w h o w e r e~ 41 1in g t o s u b s c r i b e f u r t h e r c a p i t a l t o r e p l e n i s h t h e .05 p a i d o u ti n d i v i d e n d s . T h u s t h e f r e e r e s e r v e s a t t h e e n d o f y e a r o s t o o d a t1529 .T h e e s s e n t i a l d e t a i l s o f y e a r o a r e s e t o u t i n c o l u m n I o f A p p e n -d i x I .Year z : the f i r s t c loud app ears

T h e i n t r o d u c t i o n o f t h e f i rs t c o u n t e r - in f l a t io n p o l i c y n a t u r a l l yd i s t u r b e d t h is h a p p y s t a t e o f a f fa ir s. F o r t u n a t e l y t h e c o m p a n y w a sn o t c o n v i n c e d t h a t i n f la t i o n w o u l d d i s a p p e a r a s a c o n s e q u e n c e o ft h e n e w p o li c y, a n d a t t h e b e g i n n i n g o f y e a r I i t d u l y c h a r g e dp r e m i u m s a m o u n t i n g t o I 5 2 9 , j u s t 5 % h i gh e r t h a n t h o se o f t h ep r e v i o u s y e a r. A n o t h e r f o r t u n a t e f e a t u r e w a s t h a t i n t e r e s t c o n -t i n u e d t o b e o b t a i n a b l e a t t h e r a t e o f 5 % d e s p i t e th e o f f ic ia lp r o c l a m a t i o n s t h a t i n f la t i o n w a s t o b e e l i m i n a te d .

C o l u m n 2 o f A p p e n d i x I s h o w s t h e m a i n f e a t u r e s o f y e a r x.D u r i n g t h e y e a r i n f la t i o n w a s ~ t th e r a t e o f l O % , a n d a t t h e e n do f t h e y e a r t h e p r e m i u m s o f I 5 2 9 , l e s s c o m m i s s i o n o f 2 2 9 , h a da m o u n t e d w i t h i n t e r e s t t o I 3 6 5 , a s u m i n s u f f i c i e n t t o m e e t t h ee x p e n s es a n d c l a im p a y m e n t s o f I 4 3 o ( l O % h i g h er t h a n t h e p r e v i o u sy e a r ' s f i g u r e s o f I 3 o o ) . F u r t h e r m o r e , t h e c o m p a n y d e c i d e d t o


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I 4 2 H O W I N S O L V E N T A R E W E .~

assume t ha t inflation would cont inue a t Io,/o and fix its provis ionfor outstanding claims accordingly. On the other hand, it foundthat at the end of year I interest was available at the rate of Io%,and it assumed that if inflation were to remain at that level theinterest rate would do likewise. It therefore assumed that the effectof future inflation on the outstanding claims would continue tobe exactly offset by the interest earned on the money held to paythose claims and it set up a provision for outstanding claims ofIoI2, just Io% higher than the previous year's provision of 92o.

Thus at the end of year I the free reserves, which had begun theyear at I529, had been augmented bv interest of 76 but depletedbv i i I , representing the shortfall of 65 on the paym ent s a n d 46on the provision for outst andi ng claims. The compa ny decided tha tsince it had suffered a trading loss it would make no distributionto shareholders. Thus the free reserves at the end of year I stoodat I494.Y e ar 2 : t he s k y ge t s c l oud i e r

The rise in the rate of inflation in 5"ear I had occurred towardsthe end of the year, after the decision had been made to increasethe premium rates bv the usual 5%- Thus the premiums chargedon Ist January of year 2 were I6o5. Premiums less commissionamounted to I364, which together with interest of I36 gave xSOO,compared with I716 required for payment of expenses and claimsat the end of the year after inflation at 2o%. The compan y decidedto assume t ha t inflation would con tinue a t 2O?/o, as would the rat eof interest which had just then risen to zo% from the previous levelof Io%. The provision for outstanding claims at the end of year 2was therefore ~2~4.

The free reserves of I494 at the start of year 2 were increased bvinteres t of I49 but decreased by 317 (the sffm of 216 and Io I).Again no dividends were paid to shareholders, and thus at the endof year 2 the free reserves stood at I326.Y e a r 3 : d a r k n e s s l o o m s

The premiums to be charged at the start of year 3 had to bedecided upon during 5"ear 2, and at the time this mat te r was beingconsidered the increase in the rate of inflation from Io% to ~-o%


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H O W I N S O L V E N T A R E W E ? 1 4 3

h a d n o t y e t t a k e n p l a ce . T h e c o m p a n y d e c i d e d i t w o u l d c e r ta i n l yn e e d t o i n c r e as e i ts p r e m i u m s b y IO ~o a b o v e t h e l e v e l w h i c h t h e ya p p a r e n t l y s h o u l d h a v e r e a c h e d t h e p r e v io u s y e a r ; t h i s g a v e at o t a l i n c r e a s e o f a b o u t I5 ~/o . T h e c o m p a n y w o u l d h a v e l i k e d t o g of u r t h e r - - n o t b e c a u s e i t w a s t h e n e x p e c t i n g a f u r t h e r r is e i n th er a t e o f i n f l a ti o n b u t i n o r d e r t o r e s t o r e i t s f r e e r e s e r v e s to t h e i rp r e v i o u s le v e l in r e a l te r m s . U n f o r t u n a t e l y , h o w e v e r , t h e c u r r e n tc o u n t e r - i n f l a t i o n p o l ic y d e c r e e d t h a t p a s t lo s se s c o u l d n o t b er e c o u p e d a n d t h a t p r e m i u m s c o u l d n o t b e r ai se d b y m o r e th a n I 5~ o .T h e p r e m i u m s c h a rg e d o n I s t J a n u a r y o f y e a r 3 t h e re f o r e a m o u n t e dt o I 8 4 6 .

Y e a r 3 t h u s p r o c e e d e d i n a s i m i la r f a sh i o n to y e a r 2 . P r e m i u m sa f t e r d e d u c t i n g co r h m i s si o n o f 2 76 a m o u n t e d t o I 5 7 o. W i t h i n t e r e s to f 3 14 , t h e a m o u n t a v a i la b l e a t t h e e n d o f th e y e a r f o r e x p e n s e sa n d c la im s w a s I 88 4 , c o m p a r e d w i th t h e r e q u i re d a m o u n t o f 2 2 3 I ;a s h o r t f al l o f 3 47 . T h e p r o v i s i o n f o r o u t s t a n d i n g c l ai m s w a s f i x e da t I 5 7 8 , a n d t h e f r e e r e s e r v e s fe ll f r o m I 3 2 6 t o I I 2 3 , w i t h a g a i nn o d i v i d e n d t o s h a r e h o l d e r s .

I n y e a r 3, t h e i n c r e a s e in t h e r a t e o f i n f l a ti o n h a d a g a i n o c c u r r e dn e a r t h e e n d o f t h e y e a r , t o o l a te t o b e t a k e n i n to a c c o u n t w h e nf ix i n g t h e p r e m i u m s f o r y e a r 4. I n t h e e v e n t , t h e y w e r e ra i s ed b y3 0 % t o 2 4 o o m r o u g h l y su f f ic i en t o n t h e a s s u m p t i o n o f r a t es o fi n t e r e s t a n d i n f l a ti o n o f 2 O ~ o b u t w i t h n o p r o v i s i o n f o r r e c o v e r yo f pa s t l o s s e s .Yea r 4 : th e me teo ro lo g i s t s a re co n su l t ed

D u r i n g y e a r 4 , t h e c o m p a n y d e c i d e d t o t a k e s t o c k o f t h e s i tu a t i o n .I n t h r e e y e a r s i ts p r o s p e c t i v e s o l v e n c y m a r g i n h a d f a ll en f r o mIO O ~o t o 4 7~ /o o f p r e m i u m s a n d n o l o n g e r s e e m e d s o c o m f o r t a b l yi n e x c e s s o t t h e s t a t u t o r y m i n i m u m l e v el o f 2 o~ /o . W h a t e v e r e ls em i g h t b e d o n e , i t s e e m e d t h a t t h e r e w a s a n e e d f o r f u r t h e r c a p i t a lt o s u p p o r t t h e b u s in e ss , b u t u n f o r t u n a t e l y , t h e g e n e r a l e co n o m i cs t a te o f t h e c o u n t r y a n d t h e f a c t t h a t t h e c o m p a n y h a d b e e n m a k i n gt r a d i n g l o ss es a n d d e c l a r i n g n o d i v i d e n d s in t h e p a s t t h r e e y e a r sd i d n o t m a k e t h e p r o s p e c t o f r a is i n g f u r t h e r c a p i t a l s e e m e n -c o u r a g i n g .

A n a r g u m e n t d e v e l o p e d r e g a r d i n g t h e l ik e l y f u t u r e c o u r s e o fi n fl a ti o n . O n t h e o n e h a n d t h e r e w e r e t h o s e w h o h a d g r e a t f a i th


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0-i 4 4 H O W I N S O L V E N T A R E W E .~

i n t h e a b i l i t y of t h e K i n g a n d t h o u g h t t h a t n o w t h a t h e h a d r i dh i m s el f o f t h e e c o n o m i s t s w h o s e a d v i c e h a d h a d s u c h u n h a p p yr e s u lt s h e w o u l d s u c c e e d i n re s t o r i n g t h e c o u n t r y q u i c k l y t o i t s o l ds t a t e o f u n i f o r m i n fl a t io n a t w h a t n o w s e e m e d t h e e x t r e m e l ym o d e s t r a t e o f 5O/o O n t h e o t h e r h a n d t h e r e w e r e t h o s e w h o a r g u e dt h a t t h e r e w a s n o r e a so n t o s u p p o s e t h a t t h e re c e n t t r e n d w o u l db e r e v e r s e d , a n d t h a t b y f ar t h e l ik e l ie s t o u t c o m e w a s t h a t t h e r a t eo f i n f la t io n w o u l d c o n t i n u e t o in c r e a s e y e a r b y y e a r . B e t w e e n t h e s et w o f a c ti o n s t h e r e w e r e s o m e w h o t h o u g h t t h a t i n f l at i o n m i g h t b es t a b i li s e d a t i t s c u r r e n t r a t e o f 3 o % .

A c c o rd i .n g ly it w a s d e c i d e d t o p e r f o r m c a l c u la t io n s b a s e d o nt h r e e d i f f e re n t s e t s o f a s s u m p t i o n s r e g a rd i n g t h e f u t u r e r a t e s o fi n f l a t i o n , a s f o U o w s :

Y e a r 4 5 6 7 8 9 x oP e r c e n t a g e r a t e o f ( i ) 3 0 3 3 3 o 3 3 o 3 oi n f l a t i o n i n y e a r ( 2) 2 0 I o 5 5 5 5 5

(3) 40 50 65 80 ioo 12o 15oI t w a s a s s u m e d t h a t i n ea c h c a s e t h e r a t e o f i n t e re s t o b t a i n e d i n

a n y y e a r w o u l d b e e q u a l t o t h e r a t e o f i n f la t io n i n t h e p r e c e d i n g y e a r .F i r s t f o r ec a s t: c o n t i n , i n g c l o u d y

I f t h e o u t c o m e w e r e t o c o r r e s p o n d t o A s s u m p t i o n x , w h i c h w a st h e b a s i s o n w h i c h t h e p r o v i s i o n f o r o u t s t a n d i n g c l ai m s h a d b e e nm a d e a t t h e e n d o f y e a r 3 , t h e n a n i n c re a s e i n p r e m i u m s o f a b o u t4 2 % a t t h e s t a r t o f y e a r 5, f o l lo w e d b y s u b s e q u e n t i n c r e a s e s o f3 o % , w o u l d r e s u lt i n a s t a b l e d e v e l o p m e n t s im i l a r t o t h a t o f t h eo l d d a y s o f 5 % i n fl a ti o n , b u t w i t h f r e e r e s e rv e s e q u a l t o 3 5 . 5 % o ft h e f o l lo w i n g y e a r ' s p r e m i u m s . T h e d e t a il s a re g iv e n i n A p p e n d i x 2 .I t h a s b e e n a s s u m e d t h a t e a c h y e a r th e p r o v is i o n fo r o u t s t a n d i n gc l ai m s w o u l d b e a r r i v e d a t o n t h e s a m e p r i n ci p le s a s i n y e a r s I t o 3 ,n a m e l y t h a t f u t u r e in f la t io n w o u l d b e e x a c t l y m a t c h e d b y i n t e r e s te a rn i n g s. S i n c e t h is o u t c o m e is i m p l i c it i n A s s u m p t i o n I , t h ep r o v i s i o n s a r r i v e d a t i n t h i s w a y a r e i d e n t i c a l t o t h e c o r r e c t p r o v i -s i o ns , s e t o u t a t t h e f o o t o f A p p e n d i x 2 .Second f orecas t: f i ne and sun~Lv

T h e o u t c o m e c o r r es p o n d i n g t o A s s u m p t i o n 2 is g i v en in A p p e n -d i x 3 . T h e p r o v i s i o n f o r o u t s t a n d i n g c la im s , a s sh o w n in t h e p r o -


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H O W I N S O L V E N T A R E W E ? 145

jected accounts, is again based on the assumption that futureinflation would be matched by interest earnings. The correctprovision which would ultimately turn out to have been requiredis shown at the foot of Appendix 2. Thus the provision made inthe accounts at the end of year 3 would prove to have been 2ooin excess of the amount required. If the premiums were increasedby about 42~/o at the s tar t of year 5 and then by about I2% atthe star t of year 6, followed by two years with no increase and subse-quent increases at 5%, the position would again stabilise, this timewith free reserves restored to lOO% of the following year 's premiums.Th ird forecasg: apr~ s nou s le ddluge

On assumption 3, for which the figures are given in Appendix 4,the true provision for outstanding claims at the end of year 3 wouldhave been x862, i.e. 284 greater than the provision actually made.This alone would reduce the prospective solvency margin to 839,or 35% of the premiums charged in year 4. Also, the premiumscharged at the start of year 4, less commission, were equal to only2o4o compared with 2565 required to meet the cost of claims andexpenses. This further deficiency of 525 would mean that thecompany was alreadyinso lvent; the true deficiency in the premiumswould be even greater, since the rate of interest obtainable on thefree reserves would be insufficient to maintain their real value, letalone maintain them at a constant percentage of premiums. Notonly was the company already insolvent, but by the time thehigher rate of inflation in year 4 was known, the premium ratesfor the start of year 5 would have been decided; if the increasewere around 42%, those premiums would clearly be hopelesslyinadequate. If, however, the company continued to assume, whendetermining the provision for outstanding claims at the end ofyear 4, that future inflation would be offset by future interest,the free reserves would stand at 831 and since this would be 24%of the following year's premiums the company would even thenappear from its accounts to be solvent.The end o f the Ca rma nian s tory

Unfortunately, no records have yet been found showing whathappened to inflation in Carmania in year 4 and later, nor whatI O


8/16

,. I46 H O W I N S O L V E N T A R E W E .~h a p p e n e d t o t h i s p a r t i c u l a r c o m p a n y . W h i l e e x c a v a t i o n s c o n t i n u e ,l e t u s f ir s t n o t e o n e o r t w o s i g n i f i c a n t f e a t u r e s o f t h e e x p e r i e n c eo f o u r C a r m a n i a n c o m p a n y a n d t h e n g o on t o c o n si d er i ts r e le v a n c et o t h e p r o b l e m s w e f ac e t o - d a y .

P e r h a p s t h e m o s t s t ri k i n g f e a tu r e o f t h e C a r m a n i a n s i t u a t i o n ist h a t , b a d a s th i n g s b e c a m e , t h e y c o u l d h a v e b e e n m u c h w o r s e :(a) T h e c o m p a n y e n t e r e d t h e p e r i o d o f i n c re a s in g i n f l a ti o n w i t h a

p r o s p e c t i v e s o l v e n c y m a r g in o f x o o % , f i ve t im e s t h e s t a t u t o r ym i n i m u m l e v el i n C a r m a n i a , a n d e v e n h ig h e r in r e l a ti o n t o t h em i n i m u m l ev e ls w h i c h a re c o m m o n l y f o u n d t o - d a y . I f th es o l v e n c y m a r g i n a t t h e e n d o f y e a r o h a d b e e n o n l y 4 7 % o f t h ef o l lo w i n g y e a r ' s p r e m i u m s , t h e n o n t h e , a s s u m p t i o n s m a d e i np r e p a r i n g t h e a c c o u n t s a t t h e e n d o f y e a r 3 i ts f re e r e s e r v e sw o u l d h a v e b e e n z er o.(b ) T h e c o m p a n y k e p t t h e w h o l e o f i ts m o n e y i n s h o r t - t e r md e p o s i t s , a n d t h e r e f o r e d i d n o t s u f f e r a f a ll i n t h e c a p i t a l v a l u eo f i t s a s s e t s , e i t h e r a s a r e s u l t o f t h e r i s e i n in t e r e s t r a t e s ( a sw o u l d h a v e b e e n t h e c a s e if i t h a d i n v e s t e d i n, s ay , m e d i u m -t e r m f i x e d - i n t e r e s t s t o c k s ) o r as a r e s u l t o f a fa ll i n m a r k e tv a l u e s o f o r d i n a r y s h a r e s a n d p r o p e r t y (a s m i g h t e a s il y h a v ea f f e c t e d i t i f i t h a d i n v e s t e d i n a s s e t s o f t h o s e k i n d s ) .

( c ) T h e c o m p a n y ' s c l a i m s e x p e r i e n c e r e m a i n e d r e m a r k a b l y f r e ef r o m t h e y e a r - t o - y e a r , f l u c t u a t i o n s w h i c h t h e a c t u a r i e s , w e l lv e r s e d i n t h e c l as s ic a l t h e o r y o f ri sk , h a d s a i d i t m u s t e x p e c t .T h e f i g u r e s o n w h i c h i t h a d i n p a r t t o b a s e i t s d e c i s i o n s w e r eu n d i s t o r t e d b y v a r i a t io n s in t h e v o l u m e o f b u s in e ss , t h e v o l u m eo f c l a im s , t h e t y p e s o f c l ai m s , t h e r a t e o f s e t t l e m e n t o r t h ee f f e c t i v e n e s s o f t h e c o n t r o l o f c l a i m s c o s t s ; n o r w e r e t h e r ea p p a r e n t l y a n y i n a c c u r a c i e s i n t h e r e c o r d s . I t s d i f f i c u l t i e sa r o s e s o l e l y f r o m t h e i n c r e a s e s i n t h e r a t e o f i n f l a t io n , t h ef a i l u r e o f i n t e r e s t r a t e s t o k e e p u p w i t h t h o s e i n c r e a s es , a n dt h e g e n e r al u n c e r t a i n t v w h i c h d e v e l o p e d r e g ar d in g t h e f u t u r eo f t h o s e t w o i t e m s .

T h e C a r m a n i a n c o m p a n y ' s p r o b l e m s w o u l d c l ea r l y h a v e b e e ns o m e w h a t d i m i n i s h e d i f i t h a d s u c c e e d e d in p r e d ic t i n g t h e s h a r pr is e in t h e r a t e o f i n f la t io n a n d h a d b e g u n t o r ai se it s p r e m i u m s b ym o r e t h a n 5 % e a c h y e a r w e ll b e f o r e t h e r i se i n i n fl a ti o n b e g a n - -


9/16

HOW IN SOLVENT ARE WE ? I 4 7a l t h o u g h i t m i g h t h a v e h a d d i ff ic u l ti e s o f a n o t h e r k i n d if t h ec h a r i o t i n s u r a n c e m a r k e t w e r e a c o m p e t i t i v e o n e a n d t h e o t h e rc o m p a n i e s w e r e n o t e q u a l l y p e r c i p i e n t . A n i n c r e a s e i n t h e r a t e o fi n fl a ti o n m e a n s t h a t a c o m p a n y w h o s e p r e m i u m r a t e s h a v e b e e nj u s t a d e q u a t e m u s t a t s o m e s t a g e in c r e as e i ts r a te s b y m o r e t h a nt h e c u r r e n t r a t e o f i n f l a t i o n i f i t is t o a v o i d a r e d u c t i o n i n i t s f re er e s e rv e s .

T h e f a i lu r e of t h e C a r m a n i a n c o m p a n y t o a n t i c i p a t e t h e r is e i ni n f l a t i o n l e d t o a f a l l i n i t s f r e e r e s e r v e s . T h a n k s t o i t s s t r o n gr e s e r v e p o s i t i o n a t t h e e n d o f y e a r o , t h i s f a l l c o u l d b e a c c e p t e d s ol o n g a s i t s e e m e d l ik e l y t o b e a t e m p o r a r y f e a t u r e . T h e r e al d i f f ic u l t yw h i c h c o n f r o n t e d t h e c o m p a n y w a s th a t o f p r e d ic t in g t h e f u t u r ec o u r s e o f i n f l a ti o n a n d o f i n t e r e s t r a t e s . T h e h i g h e r t h e l a t e s t r a t eo f i n f la t io n b e c a m e , t h e h a r d e r i t s e e m e d t o b e t o f o re c a s t t h e f u t u r er a te s . A s t h e r a t e o f i n f la t io n i n c r e a se d , t h e r e s e e m e d t o b e at e n d e n c y f o r i n t e r e s t r a t e s t o la g b e h i n d t h e c u r r e n t r a t e o f i n f la t io n ,b u t w h e t h e r t h a t w a s l ik e l y t o b e a p e r m a n e n t f e a t u r e o f i n c re a s in gi n f l a t i o n w a s f a r f r o m d e a r . L i k e w i s e , if t h e r a t e o f i n f l a t io n w e r et o fa il , t h e r a t e o f i n t e r e s t m i g h t e x c e e d t h e c u r r e n t r a t e o f i n f l a ti o n ,b u t w h e t h e r t h is w o u l d r e a ll y h a p p e n a n d , i f s o, t o w h a t e x t e n t ,w a s a m a t t e r f o r s p e c u l a t io n . T h e r a n g e o f u n c e r t a i n t y , e x p r e s s e di n m o n e t a r y t e r m s , w a s v e r y la r g e i n r e l at io n t o t h e p r e m i u mi n c o m e , a n d a w r o n g d e c i s io n a s to t h e l e ve l o f p r e m i u m r a t e s t oc h a r g e c o u l d q u i c k l y a c c o u n t f o r t h e w h o l e o f t h e s t a t u t o r y m i n i -m u m s o l v e n c y m a r g in .

Back to I975I n t h e p a s t f e w y e a r s , m a n y c o u n t ri e s h a v e e x p e r i e n c e d a s h a r p

r i se in t h e r a t e s o f i n c r e a s e o f p r i c e s a n d e a r n i n g s , a r i se a n a l o g o u st o , t h o u g h p e r h a p s d i f f e r i n g i n d e g r e e f r o m , t h a t w h i c h o c c u r r e di n C a r m a n i a i n y e a r s I t o 3. I n s o m e c o u n t r ie s t h e r is e h a s b e e nf o l l o w e d b y a fa U , w h i l e i n o t h e r s , s o f a r, i t h a s n o t . A s w e s u r v e yt h e w o r l d in 1 97 5 i t s e e m s d if f ic u l t to b e c o n v i n c e d t h a t t h e g e n e r a le c o n o m i c u n c e r t a i n t i e s a r e l e ss t h a n t h e y a p p e a r e d t o b e i n C a r-m a n i a .

I n t h e U n i t e d K i n g d o m , f o r e x a m p l e , n o t o n l y h a s t h e r a t e o fi n f la t i o n , m e a s u r e d b y t h e i n c r e a s e in p r ic e s o r i n e a r n in g s , r e a c h e d


10/16

148 How INSOLVENT ARE \VEsomewhere ar ound 3o0.0, but the rate of inter est obta ina ble onshor t-te rm fixe d interest in vestme nts has been as much as 15,6 to2o,/o less th an this. \Vhilst it seems difficult to imagine th at condi -tions of high negative rates of interest in real terms can continuefor long, they can create considerable clamage while they last.Insurance companies normally invest a proportion of their moneyin assets, such as ordinary shares and property, carrying a variablerate of return. The y do so partly in order to spread their inv estme ntrisks and partly in the hope that such assets will maintain or increasetheir real value in times of inflation. So indeed they may, in thelong run; over a short period, however, they may suffer a sharpfall ill their mar ket val ue --a s the y obiigingly dem ons tra ted in 1974.Our ordinary shares and property may perform well enough tomake us prosperous in I99o, but that is small consolation if we havebeen d eclared insolvent in I975 .

In place of the regularity displayed by the business of the Car-manian chariot insurance company, a modern motor insurancecompany has to contend with variations in the volume and. mixof its business, in the volume and n ature of its claims, in its staf finglevels, in the effectiveness of the contr ol over claim costs, in itsprogress in settling claims, and in the number of inaccuracies in itsrecords. All these will add to the uncertainty surrounding ourattempts to assess the present and predict the future. Fluctuationsin the claims experience associated with what we may looselydescribe as chance factors are superimposed on, and may reinforce,those due to inflation and the return on investments.

Our assessment of the provisions we need for our outstandingclaims and, still more important, of the level of premiums we needto charge in the coming year requires us to take a view as to futureinflation and link it with a careful interpretation of the figuresderived from our recent experience. It is scarcely surprising thatthe premium rates currently charged for motor insurance in theUnited Kingdom seem to reflect a wide range of optimism andpessimism. F o r ' a typical portfolio of risks, the average pre miumof the cheapest company of significant size seems to be abouttwo-thirds of that of the dearest. In a competitive market there isa clear dange r t hat the more pessimistic companies will be rel uct antto increase their ra tes to the flail ext ent tha t their fears would seem


11/16

H O W I N S O L V E N T A R E W E .~ z4 9t o j u s t i f y a n d t h a t t h i s i n t u r n w i ll e n c o u r a g e t h e o p t i m i s t s t oc o n t i n u e t o c h a r g e l o w r a t e s .

T h e f in a n ci al m a n a g e m e n t a n d s u p e r v i si o n o f i n s u ra n c e c o m -p a n i e s a r e i n g e n e r a l m a d e m o r e c o m p l e x b y f u r t h e r f a c t o rs .A c o m p a n y m a y t r a n s a c t s e v e r a l c la s se s of l if e a n d n o n -l if e in -s u r a n c e a n d m a y d o s o i n m a n y d i f f e r e n t c o u n t r i e s a n d c u r r e n ci e s .A l t h o u g h t h e c o n s e q u e n c e m a y w e l l b e a d e s i r a b l e s p r e a d i n g o fr is k s, t h e r e w i ll o f t e n b e g r e a t e r u n c e r t a i n t y b e c a u s e o f t h e d i f f i c u l t vo f o b t a i n i n g r e li a b le r e l e v a n t i n f o r m a t i o n .

T h e c l a s s e s o f n o n - l i f e b u s i n e s s d i f f e r i n t h e d e l a y i n s e t t l e m e n to f c l a im s a n d i n t h e d e g r e e t o w h i c h t h e y a r e e x p o s e d t o t h e i n -f l a ti o n ri s k: T h e d e l a y d i s t r i b u t i o n o f t h e C a r m a n i a n c o m p a n y ,

. e x p r e s s e d i n te r m s o f t h e p u r c h a s i n g p o w e r o f t h e b a s e y e a r ,h a p p e n s t o c o n t a i n t h e s a m e fi g u re s a s t h e d e l a y d i s t r i b u t i o nd e r i v e d f r o m t h e m o t o r i n s u ra n c e c l ai m s o f o n e c o m p a n y i n t h eU n i t e d K i n g d o m , a f t e r o b s e rv i n g t h e p a y m e n t s o v e r a n u m b e r o fs u c c e s s i v e y e a r s , a d j u s t i n g f o r p a s t i n f la t io n a n d s m o o t h i n g t h er e s u lt s . T h e d e f i n it i o n o f t h e d e l a y i n t e r v a l w a s d i f f e r e n t in t h a t i nt h e B r it is h c o m p a n y ' s e x p er ie n c e t h e p a y m e n t s a t " d u r a t i o n I "w e r e t h o s e m a d e d u r in g t h e c a l e n d a r y e a r i n w h i c h t h e c l a im s w e r en o t i fi e d . T h e d i s t r i b u t i o n i n t h e c a s e o f t h e C a r m a n i a n c o m p a n yis , h o w e v e r , s u f f i c i e n tl y s im i l a r t o t h e k i n d o f d i s t r i b u t i o n w h i c hc o u l d e a s il y b e f o u n d i n a p r e s e n t - d a y c o m p a n y t o m a k e i t a re a s o n -a b l e b a s i s f o r i l lu s t r a ti o n . A c o m p a n y t r a n s a c t i n g m a i n l y t h i r d -p a r t y m o t o r i n s u r a n c e , o r o n e w i t h a la r ge p r o p o r t i o n o f g e n e r a ll i a b i l i t y b u s i n e s s , w o u l d b e e x p e c t e d t o h a v e a d e l a y d i s t r i b u t i o nw i t h a m u c h l o n g e r t a i l .

T h e c u r r e n c y r i sk i n t r o d u c e s a f u r t h e r u n c e r t a i n t y . A l t h o u g ha s s e t s m a y b e m a t c h e d w i t h t e c h n i c a l l ia b i li ti e s a c c o r d i n g t oc u r r e n c y , i t i s n o t p r a c t i c a b l e t o e l im i n a t e t h e c u r r e n c y r is k b e -c a u s e o f t h e n e e d t o d r a w u p o n t h e f re e r e s e r v e s t o m e e t f l u c t u a -t i o n s .

T h e p o s i t i on s h o w n i n t h e p u b l i s h e d a c c o u n t s o f a c o m p a n y m a yd i f f e r f r o m w h a t w i l l t u r n o u t t o b e t h e r e a l p o s i ti o n , n o t o n l yb e c a u s e a c o m p a n y w i l l i n g e n e r a l n o t s u c c e e d i n p r e d i c t i n g t h ef u t u r e c o r r e c tl y , b u t a l so b e c a u s e o f a c c o u n t i n g c o n v e n t i o n s a n dp e r h a p s d e l i b e r a t e a d j u s t m e n t o f t h e f i g u re s in o n e d i r e c ti o n o rt h e o t h e r . C o m p a n i e s in th e U n i t e d K i n g d o m w o u l d , it is t h o u g h t ,


12/16

15o t lO W I N S O L V E N T A R E W E )

aim to take as their total provision for outstanding (includingincurred but not reported) claims the total sum which those claimsare estimated to cost, without discounting to allow for interestobtainable during the period before payment is made. Caution ofthis kind is entirely reasonable, but whatever the conventionsadopted in practice max" be, the underlying principles should beborne in mind.

The lessol, o f Ca rma , t i~The effects of compounding at high rates, whether of inflation

or of interest,.are so familiar to actuaries that none of the arith-m6tical results derived from the Carmanian experience will be atall surprising. The ma in message which this paper sets out to conveyis that the uncertainties associated with high rates of inflation arein monetary terms uncomfortably l a r ge in relation to the generallyaccepted minimum margins of solvency. Fluctuations attributableto the element of chance in the occurrence of claims and in theirsize (before taking inflation into account) can largely be handledby well-established procedures of reinsurance, modified perhaps bythe results of mathematical researches carried out by actuaries.Inflati on, however, is fun dame nt al ly an uninsurable risk. If in-flation reaches a very high level it soon becomes extremely difficultto find a sati sfac tory basis for takin g business decisions. 3Iuch ofthe work which has been done in elucidating the principles onwhich insurance should be conducted ,,'ill be of limited value untilwe return to a stable economic environment.

The dangers stemming from inflation serve to remind us thatwhatever the official definition of solvency may be, no insurancecompany in any country or at any time is in reality more thanconditionally solvent. While we wait for the immediate future toreveal itself, we console ourselves with the though that manyhasurance companies appear to be strong enough to ensure theirsurvival unless there is a general economic collapse, in which caseinsurance wiU not be our only problem.


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HOW INSOLVENT ARE WE ?

APPENDIX I,4 ctual Experience of Carmanian Co mp any up to

15I

End o f Year 3Year

o x 2 3 4

5 z o 20 305 5 xo 20Percentage rate of inflation in yearPercentage rate of interest in yearPercentage increase in premiums at start ofye ar 5 5 5 I5Premi ums charged at star t of yea r 1456 I529 I6o5 I846

Provision for outstanding claims at start ofye ar 876 "920 xox2 I2I 4Interest on provision for outstanding claimsat st ar t 44 46" 1ox 243Fre e reserves at st ar t of ye ar I456 x529 1494 1326Int er est on free reserves at sta rt 73 76 149 265Pre miu ms less commission at sta rt of year 1238 I3OO I364 157oInt ere st on (premiums less commission) 62 65 I36 3x4

Claims and expenses paid at end of yea r I3oo 143o 1716 2231Provision for outstanding claims at end olye ar 920 xox2 x2x 4 I578Fre e reserves at end of ye ar 1529 1494 I326 1123' ' O /93 % 72 % 47 /orospective solvency margin at end of year ioo %

3 o2400

APPENDIX 2Projected Experience o f Carmanian Co mp an y--A ssum ptio n r

Year3 4 5 6 7 8

Percentage rate of inflationin ye ar 3 30 30 30 30 3 Percentage rate of interestin ye ar 2o 30 30 30 30 3 Percentage increase in pre-miu ms at st ar t of ye ar 15 30 42.2 3 3 30Premiums charged at startof year I846 2400 34 Iz 4436 5766 7496Provision for outstandingclaims at sta rt of ye ar I214 I578 2o5I 2666 3466 4506Interest on provision foroutstanding claims atstar t 243 473 6x5 800 io4o x352


14/16

I52 HOWINSOLVENT ARE WE ?

Year3 4 5 6 7 8

Fre e res erves at st ar t of year 1326 1 I23 1212 1576 2049 2664Interest on free reserves atsta rt 265 337 364 473 615 799

Premiums less commissionat st ar t of ye ar I57O 2040 2900 3770 49Ol 6371Interest on (premiums lesscommission) 314 612 870 1131 147 1911

Clainas and expenses paid atend of ye ar 2231 2900 377 49Ol 637I 8282Provision for outstandingcla ims at end of year 1578 205 t z666 3466 45o6 5858Free reserve s at end of year 1 I., 3 1212 1576 2049 -'664 3463

Prospective solvency marginat end of ye ar 47 % 35.5 % 35.5 % 35. 5% 35.5 % 35-5 %Correct provision for out-st anding claims at end 1578 2051 2666 3466 4506 5858Correct free rese rves at end 1123 I212 1576 2049 2664 3463Correct prospective solvencymargin at end 47 % 35- 5% 35. 5% 35. 5% 35.5 % 35 .5 %

APPENDIX 3

Projected Experience of Carmanian Co m pan y--Ass um ption 2Year3 4 5 6 7 8 9

Percentage rate of inflationin yea r 30 2oPercentage rate of interestin year zo 3 Percentage increase in pre-mium at star t of year i5 3 Premiums charged at startof year 1846 24oo

Provision for outstandingclaims at st ar t of yea r 1214 1578Interest on provision foroutstanding claims atst ar t -'43 473Free reserve s at sta rt of yea r 1326 1123Interest on free reserves atst ar t 265 337

1o 5 5 5 5

20 x o 5 5 542.2 i2 o o 5

3412 3820 382o 3820 4Oli1894 2o83 2188 2297 2412

379 208 lO9 I i 5 1211592 2635 3482 3819 4OlO318 264 i75 I9i 2oi


15/16

H O W I N S O L V E N T A R E W E ?Year

3 4 5 6

153

7 8 9P r e m i u m s l e s s commissionat start of year 157 2040 29o0Interest on (p re mi um s less

c o m m i s s i o n ) 314 612 580Claims and expenses paid atend of year 223I 2677 2945Provision for outstandingclaims at end of year 1578 1'894 2083Fre e reserve s at end of yea r 1123 1592 2635Prospective solvency margin o, 69 o/t end of ye ar 47 o~,, 47 /o /oCorrect provision for out-sta ndi ng claims at end 1378 I696 I989Correc t free reserves at end I323 I79o 2729Correct prospective solvencymargin at end 55 % 52 % 71 %

3247 3247 3247 3409325 162 162 I 7O

3092 3247 3409 35792188 2297 2412 25333482 3819 4OlO 42119 1 o ~ I O 0 o / I O 0 o / I O 0 o /,' /o /o /o

2 1 8 8 2 2 9 7 2 4 1 2 2 5 3 33482 3819 4oio 42II9 1 O ~ I O 0 ~ 0 I O 0 ~ 0 I O 0 ~

APPENDIX 4Projected Experience o f Carmanian Corapany - - A s sumption 3

Year3 4 5 6 7 830 4 50 65 80 IOO20 30 4 5 65 80Percentage rate of inflation in yearPercentage rate of interest in yearPercentage increase in premiums atsta rt of year 15 3 Premi ums charged at start of year I846 2400

Provision for outstanding claims atst ar t of yea r 1214 1578Interest on provision for outstandingclaims at st ar t 243 473Free reserves at start of year I326 II23Int ere st on free reserves at star t 265 337Premiums less commission at start ofyear 157 204 0Int ere st on (premiums less commission) 3 x4 6 z 2

Claims and expenses paid at end o(ye ar 2231 3123Provision for outstanding claims atend of ye ar 1578 2209Free reserves at end of year II23 83I

4 2 .23 4 1 2


16/16

I 5 4 IIOXV I N S O L V E N T A R E W E ?

3 4Y e a r

5 6 7 8Prospective solvency .margin at en d

o f y e a r 4 7 ~/o 2 4 o~'oC o r r e c t p r o v i s i o n f o r o u t s t a n d i n g

c l a i m s a t e n d I 8 6 2 2 6 3 3C o r r e c t f r e e r e s e r v e s a t e n d 8 3 9 4 .0 7C o r r e c t p r o s p e c t i v e s o l v e n c y m a r g i na t e n d 3 5 o~, r z o ~

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