Question

If your stock portfolio raises by 5% when the 10-Year treasury market declines 3% what is the sensitivity of your portfolio compared to that of the bond market? Next, in 3 months you expect the FED will drop interest rates by 0.25%, what is your expected portfolio return on that day? (Assume demand curve is normally sloped.)

		a. The sensitivity of my portfolio is 0.6 (a positive relationship between stocks and bonds), so in 3 months time, when the FED announces they will lower rates by 0.25%, my portfolio will drop 0.15% on that day. Provided the sensitivity remains stable.
		b. The sensitivity of my portfolio is 20, so when the FED lowers rates by 3% my portfolio will rise 60%.
		c. My portfolio is not sensitive to the treasury market at all.
		d. The sensitivity of my portfolio is -1.67 (an inverse relationship between stocks and bonds), so in 3 months time, when the FED announces they will lower rates by 0.25%, my portfolio will rise 0.4175% on that day. Provided the sensitivity remains stable.

Answer 1

Sensitivity analysis, or a what-if analysis as it is sometimes called, is used to determine how much the valuation of an individual trade, and ultimately your portfolio, changes by varying an independent input. Interest rate sensitivity analysis is very important for analysing portfolio risk. An investor or corporation should ensure that the portfolio is subjected to rigorous testing to determine what the change in value might be given a change in interest rates. A key rate risk analysis is one of the most commonly used methods of evaluating interest rate risk. This analysis is essentially completing a more rigorous sensitivity analysis by varying each data input that is used in building the yield curve

As per the details stated in the question, change in portfolio return = 5%, when the change in treasury market return = -3% (negative indicates decline)

Since the demand curve is normally sloped, the sensitivity of the portfolio to treasury market interest rate movements is as follows: (linear relationship)

Sensitivity of the stock portfolio to bond market = Change in portfolio return / Change in treasury market return = 5% / -3% = -1.67

This can alternatively be expressed as follows: When the treasury market return declines by 3%, portfolio return rises by -3% * -1.67 = 5%. In other words, portfolio return and bond market return are inversely related and hence sensitivity is negative.

So, provided the sensitivity remains the same, in 3 months' time when the FED announces they will lower rates by 0.25%, my portfolio will rise 0.4175% on that day. (-0.25% * -1.67 = 0.4175%)

Hence the correct option is OPTION D.

Option A is incorrect as it assumes a positive relationship between the two variables.

Option B includes an incorrect computation of sensitivity as 20.

Option C is incorrect as it assumes that the portfolio is not sensitive to market interest changes.