An Identity Crisis for the Variable ‘R’

An interesting article questions one of the fundamental parameters of the financial theory, specifically it questions the validity of assuming a `fixed’ risk-neutral rate of interest in calculations.

Of course it is misleading to assume anything in finance is static, however modern finance theory quite inevitably requires the premise of a fixed risk-free interest rate in order to explain the future cash flows of all self-financing trading strategies in a no arbitrage world.

Modern finance has brought about numerous financial products. However, according to the complete market theory, the majority of those products are artificial constructs of the more basic securities. For example, exotic derivatives are usually modeled as complex replicates of the vanilla options. Likewise the put-call parity implies that a put and call option can be interchanged with a portfolio of the underlying stock and cash. The value of the stock is variable with the market volatility which has been subject to modelling for long; however time value of cash has been relatively straightforward and determined by the risk-free interest rate.

For decades the yield on the US treasury bills has been used as a proxy for the theoretical risk-neutral rate of interest. But in the wake of the possibility of default of the US government, and a further downgrade of the US debt by the S&P, what can serve as a proxy for a safe return in an ideally perfect risk-free world?


An Identity Crisis for the Variable ‘R’

By Christopher Faille

It might be the subject of a Sesame Street episode. “R is an important letter. It stands for Rate and Return and Risk-Free and lots of other words!” Yet, like Oscar the Grouch if deprived of his garbage can, R has lost its fixed abode…

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