Yield volatility and measurement, Financial Management

Measuring volatility is very important as it is a critical input in valuation models. In subsequent chapters we will see the importance of assumed volatility in valuing bonds with embedded options. Also, in measuring the interest rate risk of a position, a combination of duration with yield volatility is used.

Measuring Historical Yield Volatility

Standard deviation or variance is used to measure the yield volatility. We can calculate variance using historical date with the help of the following formula:

         Variance =  508_yield volatility.png                                                                         ... Eq. (1)

and

         Standard deviation = 260_yield volatility1.png

In the above formula, Xt is the observation t of variable  448_yield volatility2.png  , is the sample mean for variable X, and T is the number of observations in the sample.

Our focus is to calculate the change in the daily yield relative to the previous day's yield.

This can be computed as the natural logarithm of the ratio of the yield for two days i.e.,                          

         ln (yt/yt - 1)

Where,

         y    = Yield on day t.

         yt - 1  = Yield on day t - 1.

The relative change of daily yields computed under simple compounding and continuous compounding is almost same. But, continuous compounding is more popular among market participants.

Multiplying the natural logarithm of the ratio of the two yields by 100 scales gives us the percentage change in daily yields.

         Xt = 100 [ln (yt/yt - 1)]

Where,

         Xt   = % change in yield.

         yt    = Yield on day t.

         yt -  1 = Yield on day t - 1.

Determining the Number of Observations

The sample size, i.e., the number of observations taken, affects the calculation of daily standard deviation. It is difficult to define an ideal sample size as it always depends upon the situation in hand. For example, a portfolio manager who is more concerned about long-term volatility might use 25 days for observation whereas a trader concerned about overnight positions might use only 10 most recent trading days.

Annualizing the Standard Deviation

We can find the annualized standard deviation with the help of the formula given below:

         Daily standard deviation x 1126_standard deviation.png

There is a different view regarding the number of days in the year that is to be used in the formula given above. Some market participants use 360 days whereas some use 365 days. There are some market participants who use only trading days i.e., 260 days based on five working days in a week for 52 weeks, while some other participants deduct 10 non-trading holidays too and use 250 days.

Interpreting the Standard Deviation

Assume that standard deviation for the 15 years zero coupon bond is 14%. If the prevailing yield is 8% then the annual standard deviation will be 112 basis points (14 x 8).              

Posted Date: 9/10/2012 3:41:11 AM | Location : United States







Related Discussions:- Yield volatility and measurement, Assignment Help, Ask Question on Yield volatility and measurement, Get Answer, Expert's Help, Yield volatility and measurement Discussions

Write discussion on Yield volatility and measurement
Your posts are moderated
Related Questions
The process of securitization can best be understood by taking the following example. Assume that there exists an NBFC which has hire purchase as its major busine

What risks are associated with direct foreign investment? How do these risks differ from those encountered in domestic investment?

Hedge Funds: Hedge Funds are investment partnerships that strive for above average returns through active portfolio management and whose primary compensation is a percentage of

Product Advantages: A firm that has developed a reputation for superior products in the domestic market may find acceptance from the foreign consumers as well. Hence, such firm

Internal business risk associated with the operational efficiency of the firm. The operational efficiency differs from company to company. The efficiency of operation is reflected

QTL Tech has an issue of preferred shares outstanding with a $50 stated value that pays a dividend of 7.5%. There are 325,000 shares outstanding. QTL has not paid preferred share d

discuss an operating cycle of vegetable growing in Uganda

Q. What is Dependent Care Expenses? Dependent Care Expenses - Qualified child care expenses would allow a taxpayer this computed credit against tax. Amounts can be found on the

Financial Reports: Each person has their own perception on what a particular financial report should contain, and invariably in what they consider to be the important factors w

Q. Example on hedge fund? Hedge Fund enters agreement to sell HK$ in six month's. At expiration the Hedge Fund requires to buy spot HKD and deliver these against the short futu