Problems with numbers – Life in a PSU (Central Bank India)

Now that I have shared with you the uses of mathematics in Central Banking, let me also discuss some challenges/difficulties that the ‘use of numbers’ pose in our day-to-day office work vis-a-vis the general perception prevalent in the public domain due to improper interpretation of maths. Let me give three examples:

  • Gold Purchases: You may have come across news reports about the large current account deficit facing the country and the large import of gold being one of the important reasons for this. We often hear the argument that people buy gold as a hedge against inflation or that they are investing in a ‘safe asset’. These people use, or should one say, misuse mathematics to buttress their argument by relying on the figure of gold price appreciation in the recent past. However, to me, the data on gold price appreciation is the most convincing argument for why investing in gold is neither a hedge against inflation, nor a safe asset. Let me explain. What is the characteristic of a hedge against inflation? – it should protect your principal by giving a return slightly above the inflation rate. However, the rate of gold price appreciation in the recent past has been far in excess of the inflation rate and, hence, cannot be characterized as a hedge. In contrast, it can be termed as speculation against inflation. Similarly, the fundamental principal of risk-return trade-off states that greater returns can be achieved only by assuming greater risks. The significantly higher returns offered by gold in the past few years only indicates that the risks implicit in investing in gold have also significantly increased. Even if we calculate volatility in the gold prices over a longer time horizon, it would be far in excess of that observed in other financial assets. Hence, the rationale for investing in gold as a ‘safe asset’ is contrary to conventional wisdom of what constitutes a ‘safe investment’. Mathematics disapproves that gold is a hedge against inflation or that it is a safe asset. Unfortunately, this is not fully understood either by investors in gold or even a significant section of opinion makers and policy makers. We have no problem if proponents of gold encourage gold purchases by portraying it as a ‘speculation against inflation’ or a ‘risky investment’ (i.e. right use of mathematics) rather than by calling it as a ‘hedge against inflation’ or a ‘safe investment’ (improper use of mathematics).
  • Productivity in Banks: In banks, one of the most commonly used measures of productivity is Business per Employee. However, any student of mathematics having some basic understanding of the concept of unit and dimension will say that Business per Employee may be a good measure of productivity across space but a very poor measure of productivity over time. If we use this ratio as a measure of productivity over time in banks/financial institutions for deciding manpower issues, viz. recruitment of staff, promotions, etc., consequences would not only be erroneous but can also be dangerous. Even in deciding on the number of General Managers (GMs) or Executive Directors (EDs) to be provided to banks, policy makers are depending on the volume of business. Can we not decide on these issues in a better way by proper use of mathematics, say, based on staff expenses per 100 rupees of asset/ business or salary paid to GMs/EDs as a percentage of total assets/business of banks?
  • Financial inclusion and numbers: I am sure you have heard of our initiatives towards financial inclusion, the business correspondents, the basic banking accounts, etc. Banks often use ‘number of accounts’ and ‘number of transactions’ as two indicators for measuring progress in financial inclusion. It is common for banks to claim progress in financial inclusion stating that the number of accounts opened has gone up by 100% over a period. This use of mathematics to claim progress in financial inclusion can be terribly misleading. On delving deeper, one realizes that while 100 accounts in the previous period have, indeed, increased to 200 accounts, there is no substantive progress in terms of banking penetration and financial inclusion in real terms, since the total number of villages covered, number of BCs employed, have also increased manifold during the period. The increase in number of accounts is, thus, merely a reflection of the expanded geographical coverage and not of any improvement in banking penetration in existing locations. Similarly, the number of transactions made per month may have gone up from 50 to 100 but, simultaneously, the total number of accounts may also have gone up from 200 to 1000. Thus, this 100% increase in the number of transactions does not indicate an increase in efficiency or deepening of financial inclusion. Number of accounts per 1000 population and number of transactions per account are better mathematical ratios to judge the progress in financial inclusion.

The above three examples that I have given based on my day to day office experience, are only indicative of the irrational choices that could be made, if mathematics, as a decision making tool, is not properly used. The students of mathematics must, therefore, be extremely careful as conclusions based on improper use of numbers can lead to adverse policy decisions.

Address by Dr. K. C. Chakrabarty, Deputy Governor, Reserve Bank of India at ‘Mathemight’, a conference organized by the Department of Mathematics of the V.E.S. College of Arts, Science and Commerce, Mumbai on January 18, 2013. Assistance provided by Shri A.B. Chakraborty, Shri Sanjoy Bose and Shri Shailendra Trivedi in preparation of this address is gratefully acknowledged.
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