Jie Chao ask me a question after reading"Fooled by Randomness" by Nassim Taleb. A variant of the question is as follow; A drug test will correctly identify a drug user with positive test result 99% of the time, and will correctly identify a non-user as test negative 99% of the time. Given that 0.5 % of the underlying population are drug user, what is the probability of a person being tested POSITIVE is actually a NON-USER?
(the above example is adapted from wikipedia, look under example 1)
MCQ
So imagine now that a friend of yours went through the test and tested POSITIVE, what's the probability of him being a NON-USER?
a) 7% (i'm almost certain he's guilty)
b) 37% (i'm quite sure he's guilty)
c) 67 % (i think he's probably innocent)
d) 100% (no friend of mine would do drugs!!!)
Guess, and dun cheat by looking at wiki answer. Alternatively, it would be great if you can dig out your A levels notes and calculate it (maybe only XinHong is diligent enough to do this, heehee). Answer at the end of the post :)
Then Prof Pascale Crama gave us the classic Monty Hall problem. She let us chose from 1 of 3 envelope of which one contains 20 dollars (REAL CASH). She'll reveal an empty envelop after i've chosen one and i'll be given a chance to change my envelop. The twist is that we'll have to bid for the chance to play the game. NO ONE in the class participated at first. Damn weird, prof giving out money and almost no one wanted to play the game by giving up even 1 buck. Finally some students participated and i WON the bid at $5.
The probability of winning is about 67% (if you change the envelope) thus expected return is about $13. I'm willing to bid up to $8 to play this game. I changed the envelope after prof revealed the empty one. and I WON!!! yippee, 400% return on my initial investment!!!! since we only spent about 5 mins on this activity, can you imagine the ANNUALIZED return?!? haha. Fat hope.
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"When Markets Collide" is so engaging that i can hardly put it down over the past few days. The changing role of emerging economies in the globally will put a strain on current infrastructure. There will likely be displacement in the market and it will take some time for the world to adapt to. As a creditor to many 'developed' countries, there are many challenges that they will faced. Singapore was mentioned in the book as an exemplary example of how a country should manage its reserve. And it is also a model that many emerging economies will follow. For a good summary this changing landscape was published by Legg Mason's Maubossin article.
Reading letters by great investors that have been through market cycles allow us to see thru the valley and maintain a long term view. The Wintergreen Fund has been investing successfully globally over the years. A discussion by Bill Nygren on the 'mistakes' he has committed is particularly educational and refreshing. Click on the following paragraph to read the original commentary. And click here to read the letters to shareholders.
What did you miss on Washington Mutual?
Washington Mutual was held in all three Funds I co-manage. We sold our position during the quarter when it appeared that regulators were increasingly looking at mark-to-market implied losses, which eliminated the chance that Washington Mutual could, over time, earn back its mortgage losses. Selling was the right decision but by the time we sold, the damage had been done. Owning Washington Mutual was a big mistake for which I fully accept responsibility. Though we believed home prices had been rising at an unsustainable pace, we took comfort that previous home price bubbles had corrected with home prices plateauing for several years rather than sharply falling. Expecting that to continue, I took too much comfort in the fact that the overwhelming majority of mortgages Washington Mutual owned had balances of less than 80% of appraised value. Believing that the collateral was so valuable, I wasn’t as concerned as I should have been with softening underwriting standards. After all, if the borrower defaulted, the house could still be sold for more than the mortgage debt. After nationwide prices fell 20%—and further in hot markets—the collateral was no longer worth more than the loan, and serious losses resulted. A mortgage market previously viewed as secure became viewed as very risky. Sellers flooded the market, and prices fell sharply. Because of its leverage, Washington Mutual’s assets, marked-to-market, were no longer greater than its liabilities. Ironically, the asset we’ve always believed was under appreciated, its strong retail deposit base, is now owned by another of our holdings, JP Morgan. Though there are many lessons to be learned from this error, perhaps the most important is that in today’s economic climate, we need to consider a broader array of outcomes than we previously considered, especially for companies that employ financial leverage.
Washington Mutual was held in all three Funds I co-manage. We sold our position during the quarter when it appeared that regulators were increasingly looking at mark-to-market implied losses, which eliminated the chance that Washington Mutual could, over time, earn back its mortgage losses. Selling was the right decision but by the time we sold, the damage had been done. Owning Washington Mutual was a big mistake for which I fully accept responsibility. Though we believed home prices had been rising at an unsustainable pace, we took comfort that previous home price bubbles had corrected with home prices plateauing for several years rather than sharply falling. Expecting that to continue, I took too much comfort in the fact that the overwhelming majority of mortgages Washington Mutual owned had balances of less than 80% of appraised value. Believing that the collateral was so valuable, I wasn’t as concerned as I should have been with softening underwriting standards. After all, if the borrower defaulted, the house could still be sold for more than the mortgage debt. After nationwide prices fell 20%—and further in hot markets—the collateral was no longer worth more than the loan, and serious losses resulted. A mortgage market previously viewed as secure became viewed as very risky. Sellers flooded the market, and prices fell sharply. Because of its leverage, Washington Mutual’s assets, marked-to-market, were no longer greater than its liabilities. Ironically, the asset we’ve always believed was under appreciated, its strong retail deposit base, is now owned by another of our holdings, JP Morgan. Though there are many lessons to be learned from this error, perhaps the most important is that in today’s economic climate, we need to consider a broader array of outcomes than we previously considered, especially for companies that employ financial leverage.
Lastly, Warren Buffett wrote on op-ed on NYT. READ IT!
The ans to the mcq is C. Your friend has a 67% probability of being a non-user. So be wary of such tests results.
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