V Pattabhi Ram
The newspaper ad took Wafers’ breath away. A young woman was willing to jump down from the 25th floor of Express Towers, provided someone was willing to pay her Rs 1 lakh for the effort. “Foolish woman” said Wafers. “Why, what’s wrong with that? Is Rs 1 lakh not good enough?” asked China, sipping a mug of coke. “Or do you think she shouldn’t jump from the 25th floor?” volunteered Muscles half smilingly. “I wouldn’t jump even if they offered me a crore,” remarked Wafers. Rinku chipped in, “What if it were Rs 5 crore?” Wafers was quiet prompting China to say, “So what we are discussing is the price, not the craziness of the effort.”
For Wafers the coin clicked. The other day, her professor, explaining Return and Risk, had laid down Rule No 4, “For a given level of risk (craziness), different people look for different return (money)”. Now she understood it. The lady who had given the ad would be happy with Rs 1 lakh, Wafers would be happy only with Rs 5 crore. Even as she mulled over it, China observed, tongue firmly in cheek, “I hope you realize that your heirs, not you, may have to collect the cheque.” That gave Wafers a second crucial insight into risk. Here risk meant you wouldn’t be able to collect the return.
But “How does one quantify risk? How does one decide which option is riskier?” she wondered. Okay jumping from the 30th floor is riskier than jumping from the 25th but not every time are the options so obvious.
Rinku was animatedly talking cricket. Silly chap, she thought. “Whom should we drop, Dravid or Laxman?” was the issue. “Fall back on stat” suggested China. Rinku reeled out the numbers from the top of his head. During the last 10 innings Dravid had scored 60, 40, 50, 50, 40, 80, 20, 70, 60 and 50 for an average of 52. In contrast, Laxman had scored 110, 10, 0, 80, 20, 120, 20, 90, 10 and 60 also for an average of 52. “Whom would you retain?” prompted China. “Obviously Dravid. He is consistent,” said Rinku. “Right” said Muscles. For Wafers the coin clicked a third time. “If someone is consistent he is more reliable and hence less risky”. China helped her saying, “Mathematically, one can measure consistency by computing the standard deviation of the scores”. Dravid’s scores were closer to the mean (52) than Laxman’s. His standard deviation, and hence his risk, is lower. Muscles added, “if you plot the scores on a graph and if it resembles the graph of a heart patient’s ECG it means it carries more risk!” That was cute, thought Wafers. She now understood why standard deviation measures risk.
Even as she was salivating her newfound knowledge, Wafers heard Muscles talk of what had happened that morning at the operation theatre. The anxious patient had asked the surgeon “Doc, what are the chances of my survival?” The doctor had remarked, “The success rate is generally 10%. My previous nine patients died on the operation table itself. You are the 10th patient. You are sure to survive; 100%!” Wafers recalled what she had learnt In the classroom. That when it came to risk you assigned probability. And for that you had to rely on the past. The story of the surgeon made Wafers wonder whether too much should be read into probability.
“Is it possible to reduce risk?” Rinku asked, his mind still on cricket. Wafers recalled her professor’s words “Diversification reduces risk.” He had quoted the proverb “Do not put all your eggs in one basket” as proof. But had nattily added Mark Twain’s remark, “put all your eggs in one basket and watch the basket grow!” The message: If you want to maximize return bet on your best product; if you want to minimize risk diversify. A smart aleck in the class had asked, “Sir, is that why you studied both CA and ICWA?” And had quickly supplied the logic. “So that if you did not get through CA you could atleast get through ICWA.” The professor was stumped but admitted that even he couldn’t have explained diversification better.
Not every risk is diversifiable, Wafers had told herself. Getting married is a risk. But you cannot diversify by marrying more! She didn’t raise that point in the class. She also told herself that while the CA-CWA was a cute example, it didn’t quantify the extent of risk reduction. She turned to the brainy IIT-MMC duo of China and Muscles for help. And they didn’t disappoint her. They told her a story.
Muscles’ distant cousin lived in a god- forsaken place that had only one season, summer or winter, throughout the year. The cousin wanted to set up either a coffee pub or a soft drink joint. China suggested that he do a market survey before taking the plunge. Wafers remembered her professor’s remark, “Its not enough to have a good idea; there must be a market for the good idea”. A week later the cousin had come back. Market survey had suggested that if it were summer, the return from soft drink would be 40% while that from coffee would be 10%. If it were winter, the return from soft drink would be 10% while that from coffee would be 40%. “How would you know whether it would be summer or winter”, Wafers asked China. “I wouldn’t” said China. Her professor had said, “there are only probabilities, not certainties in life.”
Muscles continued with the tale. “We asked my cousin to log on to the met department’s website for statistics relating to the last 100 years.” He had come back with the answer. “50 years summer and 50 years winter. So the probability was 50:50” Back of the envelope calculations indicated that the expected return from soft drink was 25%. [(0.5 X 40) + (0.5 X 10)]. Ditto for coffee pub business. The soft drink business carried risk because the return could be either 40% or 10% while the mean was 25%. Since this was true for coffee business too, the risk was identical.
“So what did you do?” asked Rinku. “Did you toss a coin and decide?” China said, “We asked Muscles’ cousin to put half his money in soft drink and half in coffee pub”. Muscles added, “Our logic was simple. In summer my cousin would get 40% from coffee and 10% from soft drink. Since he had put 50% of his money in either business his summer return would be 25%. [0.5 X 40+ 0.5 X 10] Ditto would be the winter return. And since the probabilities of summer and winter were 50:50 the overall return would be 25%. [0.5 X 25 + 0.5 X 25].” Wafers understood. Whether summer or winter the expected return would be 25%. Diversification had eliminated risk.
A mix of coffee and coke had helped her understand more about risk. How would such a cocktail taste she wondered?
First published in the Hindu Business Line