Risk-value relationship

This post was a response to a student's post about risk.

World Risk 2006

http://gadgetmaniac.mail2web.com/2006/04/2006-political-economic-risk-map/

Yes, that is exactly how it is calculated. To calculate the expected rate of return using the Capital Asset Pricing Model (CAPM http://en.wikipedia.org/wiki/Capital_Asset_Pricing_Model) we first determine the risk free rate of return. Usually, people select something like the rate paid on US treasuries as the risk free rate of return for the US dollar. LIBOR (London Interbank Offered Rate http://en.wikipedia.org/wiki/LIBOR) is often used as a proxy for the risk free interest rate. Since each currency has its own unique risk free rate, LIBOR offers the rates for major currencies like the dollar and the Euro. The risk free rate of return represents the time value of money separate from risk. We assume that to have money stay at its equivalent value over time, it has to receive the risk free rate, which primarily compensates for inflation and the lender’s opportunity cost. A separate factor in the CAPM is risk portion of the return. To isolate the risk portion of the return, we calculate the rate of return paid in the market as a whole minus the risk free rate. As a proxy for the average rate of return in the economy as a whole, we select a broad measure. In the US, it would be something like the average rate of return on the S&P 500 minus the dollar LIBOR rate. This represents that average return paid in the US market for risk.

Beta (β) is the ratio of the average market risk to the risk of the particular asset or project that we want to value. The beta calculations for stocks can be found on Google Finance (e.g. General Electric http://finance.google.com/finance?q=NYSE:GE). Thus, we times the average market risk with β to determine the risk portion of the rate of return that must be added to the risk free rate in order to obtain the total expected rate of return associated with a specific project or asset. This is the CAPM formula. Expected rate of return equals the risk free rate plus beta times the risk portion of the average rate of return in the market.

$E(R_i) = R_f + \beta_{im}(E(R_m) - R_f).\,$

The expected rate of return can then be used in a Net Present Value (NPV) calculation, along with the cash flows expected to be produced, to determine the value of a project or asset. http://en.wikipedia.org/wiki/Net_present_value

$\mbox{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1+r)^{t}} - {C_0}$

As you can see, the expected rate of return calculated by the CAPM equation goes in the denominator of the NPV equation. This means that there is an inverse relationship between risk and value. The greater the risk associated with a particular project, the lower its value. Likewise, the lower the risk associated with a particular project, the higher its value. Thus, asset values in a high risk country will be lower than asset values in a low risk country. War, the absence of property right and the rule of law, unfavorable geography, unpredictable political environment, etc. all add risk to a country and drive down asset values. This is why a factory in Baghdad will be worth less than an identical factory in Dubai, even if they are projected to create identical cash flows. Because there is more risk inherent in doing business in Baghdad, it will be poorer than Dubai, even if all of its assets were otherwise identical.

		October 7, 2007 *Why Risk Kills Value*
	This post was a response to a student's post about risk. World Risk 2006 http://gadgetmaniac.mail2web.com/2006/04/2006-political-economic-risk-map/ Yes, that is exactly how it is calculated. To calculate the expected rate of return using the Capital Asset Pricing Model (CAPM http://en.wikipedia.org/wiki/Capital_Asset_Pricing_Model) we first determine the risk free rate of return. Usually, people select something like the rate paid on US treasuries as the risk free rate of return for the US dollar. LIBOR (London Interbank Offered Rate http://en.wikipedia.org/wiki/LIBOR) is often used as a proxy for the risk free interest rate. Since each currency has its own unique risk free rate, LIBOR offers the rates for major currencies like the dollar and the Euro. The risk free rate of return represents the time value of money separate from risk. We assume that to have money stay at its equivalent value over time, it has to receive the risk free rate, which primarily compensates for inflation and the lender’s opportunity cost. A separate factor in the CAPM is risk portion of the return. To isolate the risk portion of the return, we calculate the rate of return paid in the market as a whole minus the risk free rate. As a proxy for the average rate of return in the economy as a whole, we select a broad measure. In the US, it would be something like the average rate of return on the S&P 500 minus the dollar LIBOR rate. This represents that average return paid in the US market for risk. Beta (β) is the ratio of the average market risk to the risk of the particular asset or project that we want to value. The beta calculations for stocks can be found on Google Finance (e.g. General Electric http://finance.google.com/finance?q=NYSE:GE). Thus, we times the average market risk with β to determine the risk portion of the rate of return that must be added to the risk free rate in order to obtain the total expected rate of return associated with a specific project or asset. This is the CAPM formula. Expected rate of return equals the risk free rate plus beta times the risk portion of the average rate of return in the market. $E(R_i) = R_f + \beta_{im}(E(R_m) - R_f).\,$ The expected rate of return can then be used in a Net Present Value (NPV) calculation, along with the cash flows expected to be produced, to determine the value of a project or asset. http://en.wikipedia.org/wiki/Net_present_value $\mbox{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1+r)^{t}} - {C_0}$ As you can see, the expected rate of return calculated by the CAPM equation goes in the denominator of the NPV equation. This means that there is an inverse relationship between risk and value. The greater the risk associated with a particular project, the lower its value. Likewise, the lower the risk associated with a particular project, the higher its value. Thus, asset values in a high risk country will be lower than asset values in a low risk country. War, the absence of property right and the rule of law, unfavorable geography, unpredictable political environment, etc. all add risk to a country and drive down asset values. This is why a factory in Baghdad will be worth less than an identical factory in Dubai, even if they are projected to create identical cash flows. Because there is more risk inherent in doing business in Baghdad, it will be poorer than Dubai, even if all of its assets were otherwise identical.