Application of Volatility in Portfolio Construction Applied Mathemati

Question: Explain about the Report on Application of Volatility in Portfolio Construction for Applied Mathematics and Physics? Answer: 1) Bond Yield to maturity Annually Semi annually Face value 1000 1000 Years to maturity 7 7 Annual coupon rate 5.25% 5.25% Effective coupon rate 5.25% 2.63% NPER 7 14 Frequency of payment 1 2 Value of bond 1200 1200 Payment 52.5 26.25 Present value -1200 -1200 Future value 1000 1000 Yield to maturity 17% 9% KUEHN and Schmid (2014) saw that yield from the bond at the time of maturity provides the money in hand of the investors. The different payment timing of the bond may yield different percentage at the maturity of the same. The yield provides the insights of return of the investment, which is very important for the investors for making investment decision. The above example showed that for annual and semi-annual payment of interest rate has changed the yield rate. The relationship of yield rate and payment term of interest is inverse (Becker and Ivashina 2014). 2) The graphs below showed that the return from PHLX index is higher than Dow Jones and so the risk of making investment. The risk-return parity is maintained in this case throughout the period of investment. The volatility of the high yield index is high as in line with the theoretical model of risk-return trade-off (Ha, Liu and Zheng 2015). In this context, the investor is risk averse. Thereby, PHLX index must be avoided for making any investment. However, Dow Jones is suitable for making conservative investment decision. DOW Jones Industrial average PHLX Gold/Silver Sector Index Return 0.05 0.10 Standard Deviation 0.186373263 0.299016301 Weight 0.5 0.5 Correlation -0.001170892 Portfolio Return 0.076752089 Portfolio Variance 0.031003809 Portfolio Risk 0.176078986 In case of separate measurement of the investment return and risk assessment of the investment, we could see that Dow Jones has low volatility compare to PHLX index. The return from the Dow is lower than the PHLX index. The portfolio constructed with an equal investment in both of the index has shown that volatility is low due to merged portfolio constructed by two different entities. Further, the return from the investment through portfolio was medium with a lower risk associated with the investment. The trade-off between risk and return is the basic relationship between the two where the investors may find the return from the risky product much higher. Huang, Zhou and Zhu (2012) observed that trade-off maintains the basic principle of the investors taking more risk to gain more return from their investment. From the below figure, we can see that relationship where for the higher return the measured risk was high too. 3) CAPM return of MSFT 12% CAPM return of Mondelez International 8% With the calculation of CAPM modelling, the return from the investment in Microsoft was seen as 12% while return from Mondelez was 8% only. The risk associated with the shares of MSFT was higher than Mondelez International. The regression model has shown that risk in MSFT is higher than that of the Mendelez. However, the value of beta in both the measurement techniques was not same for both the companies. The regression equation for predicting the theoretical return is as follows: Y(return from MSFT) = .0266 + 0.728 * X (price of share) [0.728 is the risk of investment in the share of MSFT] Y(return from Mendelez) = .086 + 0.362 * X (price of share) [0.362 is the risk of investment in the share of Mendelez] 4) The volatility in the call option has been started with 15% for getting the striking price of the call. The measurement provided us the price of $4.63 for 15% volatility. However, the goal seek application let us know the exact rate of volatility of the call price for $5.8. The value of the implied volatility required for this case is 19%. References Becker, B. and Ivashina, V., 2014. Reaching for yield in the bond market.The Journal of Finance. Ha, M., Liu, G.Z. and Zheng, L., 2015. Application of Volatility in Portfolio Construction.Journal of Applied Mathematics and Physics,3(07), p.808. Huang, X., Zhou, H. and Zhu, H., 2012. Assessing the systemic risk of a heterogeneous portfolio of banks during the recent financial crisis.Journal of Financial Stability,8(3), pp.193-205. KUEHN, L.A. and Schmid, L., 2014. Investment Based Corporate Bond Pricing.The Journal of Finance,69(6), pp.2741-2776.