Private Wealth Management puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 3
- Topics
- 13
- Hard
- 30
009A client regrets missing two stocks on his 20-stock watchlist that doubled last year. Of the other 18, five halved and thirteen ended flat. What would an equal stake in all 20 have returned?Wealth management
Try it first
Before you add it up: what did the whole watchlist return?
Show the worked solution
An equal stake in all 20 would have lost 2.5%. Put Rs 1 lakh in each, Rs 20 lakh in total. The two doubles end at Rs 4 lakh, the five halved end at Rs 2.5 lakh and the thirteen flat end at Rs 13 lakh, which is Rs 19.5 lakh. The winners he remembers were two picks out of a list that lost money as a whole.
Why does the regret feel bigger than the numbers?
Think of someone who says they almost bought a winning lottery ticket because the number was one digit off their birthday. Every number was one choice among many; only the winner gets remembered. Hindsight picks the winners after the result is known, which is a choice the client never actually had at the time. This is hindsight biasThe tendency to believe, after an outcome is known, that it was predictable and that you would have acted on it., and it makes the missed gains feel certain.
The client remembers two stocks that doubled, but an equal Rs 1 lakh in each of the 20 on his watchlist would have turned Rs 20 lakh into Rs 19.5 lakh, a loss of 2.5%. How do you use the number with the client?
Turn the regret into the decision he actually faced. At the start of the year he had twenty names and no way of knowing which two would double. The honest benchmark for a missed opportunity is the whole set of choices available at the time, not the best one in hindsight. On that benchmark his inaction cost nothing: holding cash lost nothing, while the list lost 2.5%.
The relationship2, 5, 13 the number of stocks that doubled, halved and stayed flat 20 the whole watchlist, equally weighted What it says in wordsThe equal-weight return is the simple average of the 20 returns.Note the arithmetic quirk it hides. A double and a halving look like mirror images, but the double adds Rs 1 lakh while the halving takes away only Rs 50,000. Five halvings still outweigh two doubles here, and the adviser who can show that in rupees wins the conversation.
Where candidates lose it
The trap is anchoring on the two doubles and guessing a positive return. Candidates who do this repeat the client's own bias back to him, which is the opposite of the job.
The second loss is getting minus 2.5% and not saying what it means for the conversation. The interviewer wants the reframing: judge a decision by the choices available at the time.
What the interviewer asks next
- If he had bought any two stocks from the list at random, what is the chance he would have picked both winners?
- How would you respond if he wants to buy only last year's winners now?
- What other bias sits next to hindsight in a client's review of his own record?
085A client bought a stock at Rs 500 and it now trades at Rs 300. He says he will sell only once it gets back to Rs 500. What return does he need just to get there, and what is wrong with the plan?Wealth management
Try it first
What rise takes Rs 300 back to Rs 500?
Show the worked solution
He needs 66.7%, and the plan anchors on a price the market does not care about. Getting from Rs 300 to Rs 500 is a rise of 200 on 300. At 12% a year that is about 4.5 years. The purchase price is history; the question is whether he would buy the stock at Rs 300 today.
Why is 66.7% bigger than the 40% he lost?
A shirt marked down from Rs 500 to Rs 300 is 40% off. Marking it back up to Rs 500 is a 66.7% rise, because the markup is taken on the lower price. A percentage recovery is measured from the lower base, so the gain needed to recover always exceeds the loss suffered.
The relationshipg the rise needed to get back to the purchase price n years to get there at 12% a year What it says in wordsThe rise needed is the purchase price over today's price, less one; at 12% a year it takes about four and a half years.The Rs 500 purchase price sits above today's Rs 300 like an anchor, and reaching it needs a 66.7% rise, about 4.5 years at 12% a year, although the market sets no target from what the client paid. What is wrong with waiting to get back to Rs 500?
AnchoringLeaning on a reference number, here the purchase price, when judging a value that should not depend on it. on the purchase price makes a past number decide a future choice. The stock's next return is the same whether he bought at Rs 500 or Rs 200, so the only live question is whether Rs 300 of this stock is the best use of Rs 300 today. Holding a loser to avoid admitting a loss, while selling winners early, is a well documented pattern called the disposition effect.
Say it kindly. Nobody enjoys booking a loss, and the job is not to tell the client he was wrong. Ask him whether he would buy it today at 300; if the answer is no, he is holding it only because of a number from the past. A booked loss may also offset other gains for tax, which is a real reason to act rather than wait.
Where candidates lose it
The fast wrong answer is 40%, the size of the fall. It measures the recovery on the old base, and the interviewer hears that you would not spot the same error in a client's thinking.
The bigger loss is doing only the arithmetic. The question asks what is wrong with the plan: name anchoring, give the one question that breaks it, and say it without making the client feel foolish.
What the interviewer asks next
- The stock falls further to Rs 250. What rise is needed now?
- Why do investors tend to sell winners too early and hold losers too long?
- How would you raise this with a client who is emotionally attached to the stock?