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The Actuary The magazine of the Institute & Faculty of Actuaries

A study in grey

It is some time since I last tried the public’s patience with these sketches of mine, and so it is with no little trepidation that I find myself sitting here, fountain pen in hand and inkpot at my elbow, attempting to set before you the facts of what I have called ‘The Adventure of the Analysis of Surplus’. I fear that my already corroded abilities as a narrator have quite rusted over through years of inactivity; if such a suspicion proves subsequently to be borne out in experience, I can only request that you accept my apologies.It was in the summer of 1904 that my friend and I were called to the home of Mr Ephraim Wobblegoose. On the way, Holmes called my attention to an individual standing on the side of the street.‘What do you make of that character, Watson?’ said he. ‘By a cursory inspection, I should deduce that he is a smoker.’‘Goodness gracious, Holmes!’ I cried. ‘You never cease to amaze me! You deduce from a single glance, not only that his name is Watson, but also that he is a smoker. How? Was it from the colour of the mud on his trousers, or by the way that he parted his hair? Holmes, your powers are almost supernatural!’‘No, no. You misunderstand me. Your name is Watson, not his. And when I see a man standing with a cigarette in his mouth and smoke billowing out of his nostrils, I know either that he is a smoker, or else that he is a species of dragon. The latter of these I think we can discount as a possible explanation.’‘When you explain it, Holmes, it all seems so simple,’ I said, ‘And I feel quite an idiot for not having seen it myself.’‘Quite so, Watson. But wait, we have reached our destination. Who is this gentleman? I rather fancy that it is our client.’We were greeted by a perspiring middle-aged man who appeared to be something of, if not all of, a twitter. I made a private diagnosis of mild brain-fever. ‘And you are Mr Wobblegoose, I take it?’ said Holmes.‘No, I am his butler, Caffrey,’ replied the man. ‘See, it’s written here on my name badge in large letters. And twice underlined in red. Would that Mr Wobblegoose were here to greet you. But Mr Wobblegoose is dead.’Holmes’s eyes began to twinkle.‘Mr Wobblegoose had been behaving strangely recently,’ said Caffrey. ‘He had taken to wearing a different moustache each day. Sometimes brown, sometimes black. Sometimes red. And always different lengths. This morning I found him… well, you had better see for yourself.’Caffrey led us to the library, in which Mr Wobblegoose’s corpse lay slumped over a desk, a scrap of paper clutched in its greying right hand, a dagger in its left, and a trickle of blood from the chest. I made a private diagnosis of advanced brain-fever. Holmes gently eased the scrap of paper from the man’s stiffened fingers, and read.‘Salary strain, four hundred and twelve… Withdrawal strain, ninety… I take it that Mr Wobblegoose is an actuary?’ he asked Caffrey.‘Exactly so,’ said Caffrey, ‘Although how you knew that is quite beyond me…’‘There were a number of clues,’ said Holmes. ‘The colour of the mud on his trousers. The way he parts his hair. Also the fact that it says so on the plaque outside the front door. But this piece of paper here, this “analysis of surplus”, appears to be the reason why he took his life. We must study it in detail. Each of these entries represents a source of profit or strain for a pension scheme. Tell me, Watson, you know my methods. Study it. What do you see?’‘Nothing, Holmes.’ – ‘Nothing!’ – ‘I see nothing, Holmes.’‘What about the the curious incident of the deaths in deferment?’Caffrey scanned the document.‘There were no deaths in deferment,’ he said.‘That is the curious incident to which I refer,’ said Holmes. ‘Do you not find it unusual that none of the deferred pensioners passed away in the inter-valuation period?’‘What is this item here?’ I asked, ‘“Miscellaneous”?’‘Oh that’, said Holmes, clearing his throat, ‘Well, once you have discounted each source of profit or loss – at an appropriate discount rate – then whatever remains, no matter how large, is miscellaneous. I rather fancy,’ he said, warming to his theme, ‘that Wobblegoose here had been creating false identities in the names of the deceased deferred pensioners and siphoning off their funds. To do this, he would have required a vast number of disguises – hence the moustaches. Now, look at this singular feature – a withdrawal strain. At first sight a bit surprising? But observe that we are using a dual discount rate technique, where we have different discount rates prior to, and after, withdrawal from active service. Hence, when someone withdraws, you get the curious effect of a withdrawal strain arising. Ha! Fascinating! Fascinating, eh?’ he said, turning to look at Caffrey. But Caffrey had left the room.