# Yield to Call – Definition

### Yield To Call Definition

The Yield to Call refers to the interest that a bond or note will pay if the investor purchases and holds the instrument until its call date.

A bond has a purchase price based upon the present value of future interest payments (coupons) and return of principal at maturity. Many issuers of bonds (particularly corporations) will include the option to repurchase (or call) the bond at a date prior to the maturity date (the date when the principal is repaid). The price to call the bond is known as a “call price”.

The Yield to Cal is calculated using the coupon rate (interest rate), the number of payment periods until the call date, and the current market price. The equation for yield to call is as follows:

P = (C / 2) x {(1 – (1 + YTC / 2) ^ -2t) / (YTC / 2)} + (CP / (1 + YTC / 2) ^ 2t)

Where,

P = the current market price

C = the coupon payment

CP = the call price

t = the number of coupon payments remaining until the call date

YTC = the yield to call

This formula makes it very difficult to solve for YTC by hand. This process is made far easier with excel.

### Academic Research on Yield to Call

• ·       High-yield bond default and call risks, McDonald, C. G., & Gucht, L. M. V. D. (1999). Review of Economics and Statistics81(3), 409-419. This research work explains the call behaviour as well as the high-yield bond using a competing risk hazard model that estimates the impact of the bond age, characteristics of the business and issue specific properties on both events. The result from these analyses indicates that the default rates increases and decreases while the call rate increases and level off. Call rate is influenced by the maturity and issues size while coupon size and rating affects the default risk.
• ·       THE EFFECT OF CALL RISK ON CORPORATE* BOND YIELDS, Jen, F. C., & Wert, J. E. (1967). The Journal of Finance22(4), 637-651. This paper explains the various effect of the call risk on corporate bond yield. It also explains the influence of the call risk on the yield spread.
• ·       Valuation of American call options on dividend-paying stocks: Empirical tests, Whaley, R. E. (1982). Journal of Financial Economics10(1), 29-58. According to this research paper, the comparison between the pricing performance of the valuation equation for American call on the stock with known dividend and the two suggested estimated methods. This paper examines the options market efficiency which is a new method that has been adopted in the product and labour market. The estimated result obtained by substituting the stock price net of the present value of the escrowed dividends into black Scholes model is used to influence the correlation between prediction errors and other factors.
• ·       An empirical examination of the Black‐Scholes calls option pricing model, MacBeth, J. D., & Merville, L. J. (1979). The Journal of Finance34(5), 1173-1186. This research analysis explains the observed results of the Black-Scholes call option pricing model and the effect of this result on the market forces.
• ·       On-call processing delay in high speed networks, Hwang, R. H., Kurose, J. F., & Towsley, D. (1995). IEEE/ACM Transactions on Networking (TON)3(6), 628-639. This paper explains the significant burden placed on the processing data of the network since admission and routing policies will be totally intensive than those in the present network. According to this paper, the delay in these various elements is caused by their power and other variable factors such as propagation delays, routing algorithm and network topology. The main aim of this research work is to distinguish the behaviour of these factors on the accepted call and setup time. This behaviour is tested for three sequential routing schemes and two flooding routing scheme using a different form of admission control and network parameters.
• ·       The Value of the Call Privilege, Winn, W. J., & Hess Jr, A. (1959). The Journal of Finance14(2), 182-195. This research work explains in-depth the value of the call privilege and how it influences the yield spread and various sector in the economy.
• ·       Daily and intradaily tests of European put-call parity, Kamara, A., & Miller, T. W. (1995). Journal of Financial and Quantitative Analysis30(4), 519-539. According to this paper, methods used by existing studies of the put-call parity reports the frequent substantial violation. One of the most important factors to note when interpreting this result is that all of these studies mainly investigates the American option. So, this paper concluded that to an extent, the observed put-call parity violations are either due to market inadequacies or due to the value of early exercise. This paper observes violations that are smaller and much less frequent than the studies using American methods.
• ·       THE VALUE OF CALL DEFERMENT ON A BOND: SOME EMPIRICAL RESULTS1, Pye, G. (1967). The Journal of Finance22(4), 623-636. This paper explains the value of the call deferment on a bond. This result analyzed several empirical results to obtain values of the call deferments in other to estimates and compare them and find their relationship with the call-parity violation.
• ·       Call feature and corporate bond yield spreads, Samet, A., & Obay, L. (2014). Journal of Multinational Financial Management25, 1-20. This paper explains that the callable bond provides a higher yield compared to the non-callable bonds. This paper tests the call bond in a wider framework simultaneously controlling the bond level, country-level variables and the firm level. This analysis adopts the use of an international sample of 13,936 bonds that were issued between 1991 and 2007 and according to the analyses; the callable bond was found to have a positive call spread which is economically and statistically significant. Also, the junk callable bond was found to have a higher call spread than the investment-grade callable bond which is even with the signalling theory.
• ·       The effects of domestic and foreign yield curves on the value of currency American call options, Choi, J. J., & Hauser, S. (1990). Journal of Banking and Finance14, 41-53. This research work examines the degree of responsiveness of the values of foreign currency on the American call option in relation to the foreign and domestic term structure of their interest rate. The pricing of the currency option models is equalled with and without the term of structure effect. According to this paper, it was analyzed that there are existing biases in the significant pricing if the flat yield curves are assumed and if the different shapes of the foreign and domestic yield curve have an influence on the currency option price.
• ·       An empirical examination of call option values implicit in US corporate bonds, King, T. H. D. (2002). Journal of Financial and Quantitative Analysis37(4), 693-721. This paper examines the value of the call option implicit in the United State corporate bond from 1973 to 1994. The average value of the call option is estimated to be 2.25% of par. Until a year before the first call date, call value always remains zero or close to zero. According to the paper, the bases of the call values are determined and the result shows that the bond of firms that have aggressively called in the past has a larger call value. Smaller slopes of the yield curve, lower interest rate and higher interest rate volatility are all factored that leads to a larger call value. This result also shows that the call value increases with an increase in the time to maturity I the callable period and vice versa.
• ·       Convertible bond design and capital investment: The role of call provisions, Korkeamaki, T. P., & Moore, W. T. (2004). The Journal of Finance59(1), 391-405. This paper hypothesized that if a firm issues convertible securities to make sequential investments easy to achieve, the securities have to be contrived to achieve enough flexibility to contain the timing of follow-on investment. This paper examines the call provisions in convertible bonds and suggests that the firms having investment options expected to expire sooner rather than later offers weaker call protection. And this situation is influenced by firms that have greater investment immediately after issuance than those firms issuing convertibles with stronger protection.