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Posted in Business, Finance and tagged Business Finance

Derivation of yield curve construction formula with tenor basis spread

If LIBOR is truly risk-free, the swap of 3-month LIBOR and 6-month LIBOR should be tradable with zero spread. However, LIBOR takes into account the credit risk of banks, and tenor swaps are exactly the transactions that swap the risk of 3-month LIBOR and 6-month LIBOR. After the financial crisis, the risk of bankruptcy, that is, the difference in tenor, was conscious, and when swap 3-month LIBOR and 6-month LIBOR, the 3-month LIBOR side began to trade with a non-negligible spread.

After all, after supplementing the discount factor and tenor spread in 0.25 year increments, the future 3-month LIBOR can be calculated as follows (Nakahara, 2013).

\begin{eqnarray} L_{forward}^{3MWorld}(t,t_{i},t_{i+0.25})=\frac{1-DF(t,t_{i+0.25})-TS^{3M-6M}(t,t_{i+0.25})\times\sum_{j=1}^{4i+1}{DF(t,t_{\frac{j}{4}})\times\frac{1}{4}}}{DF(t,t_{i+0.25})\times\frac{1}{4}}+\frac{-\sum_{j=1}^{4i}{L_{forward}^{3MWorld}(t,t_{\frac{j-1}{4}},t_{\frac{j}{4}})\times DF(t,t_{\frac{j}{4}})\times\frac{1}{4}}}{DF(t,t_{i+0.25})\times\frac{1}{4}}． \end{eqnarray}

However,

  • $L(t,T)$: Observable LIBOR at time point $t$ maturity $T$
  • $L_{forward}^{3MWorld}(t,t_{0},t_{0.25})=L(t,t_{0.25})$
  • $L_{forward}^{3MWorld}(t,t_{i},t_{i+0.25})$: A 3-month LIBOR with a reset date of $t_{i}$ and a maturity of $t_{i+0.25}$ as seen from the point in time $t$
  • $TS^{3M-6M}(t,T)$: Tenor spread when swapping 6-month LIBOR for 3-month LIBOR at time $t$ and maturity $T$

In this article, we try to derive the equation (1). At this time, the evaluation formula of the JPY tenor swap is expressed as follows (Takahashi, 2010)．

\begin{eqnarray} \sum_{n=1}^{N}\delta_{n}(E_{t}[L(T_{n-1},T_{n}+\tau_{N}]P_{t,T_{n}})=\sum_{m=1}^{M}\delta_{m}E_{t}[L(T_{m-1},T_{m}]P_{t,T_{m}}． \end{eqnarray}

However,

  • $N=2M$
  • $L(T_{n-1},T_{n})$: LIBOR with a reset date of $T_{n-1}$ and a maturity of $T_{n}$
  • $P_{t,T_{n}}$: Zero coupon bond price with maturity of $t$ at time $ T_{n}$
  • $\delta_{n}$: Interest calculation period
  • $\tau_{N}$: Tenor spread when swapping 6-month LIBOR for 3-month LIBOR at time $t$ and maturity of $T (= T_{N} = T_{M})$

Now, we want to derive 3 months LIBOR, that is, $E_{t}[L(T_{N-1}, T_{N}]$, therefore expand the left side of the expression (2) as follows.

\begin{eqnarray} \sum_{n=1}^{N}\delta_{n}(E_{t}[L(T_{n-1},T_{n}+\tau_{N}]P_{t,T_{n}})=\sum_{n=1}^{N-1}\delta_{n}(E_{t}[L(T_{n-1},T_{n})]P_{t,T_{n}}+\delta_{N}E_{t}[L(T_{N-1},T_{N})]P_{t,T_{N}}+\sum_{n=1}^{N}\delta_{n}\tau_{N}P_{t,T_{n}}． \end{eqnarray}

On the other hand, the relationship between Libor and the discount rate is

\begin{eqnarray} E_{t}[L(T_{m-1},T_{m})]=\frac{1}{\delta_{n}}\left(\frac{P_{t,T_{m-1}}}{P_{t,T_{n}}}-1\right)． \end{eqnarray}

Since it is represented by, the left side of the expression \label{tenor} can be expanded as follows.

\begin{eqnarray} \sum_{m=1}^{M}\delta_{m}E_{t}[L(T_{m-1},T_{m}]P_{t,T_{m}}=P_{t,T_{0}}-P_{t,T_{M}}=1-P_{t,T_{M}}． \end{eqnarray}

After all, JPY 3 months LIBOR, ie $E_{t} [L(T_{N-1},T_{N}]$, is given below.

\begin{eqnarray} E_{t}[L(T_{N-1},T_{N}]=\frac{1-P_{t,T_{M}}-\sum_{n=1}^{N}\delta_{n}\tau_{N}P_{t,T_{n}}}{\delta_{N}P_{t,T_{N}}}+\frac{-\sum_{n=1}^{N-1}\delta_{n}(E_{t}[L(T_{n-1},T_{n})]P_{t,T_{n}}}{\delta_{N}P_{t,T_{N}}}． \end{eqnarray}

Reference

  • Nakahara, G.，2013. LIBOR and OIS discount that can be seen in EXCEL (In Japanese)
  • Fujii, M.，Shimada, Y. and Takahashi, A.，2010. “A Note on Construction of Multiple Swap Curves with and without Collateral”， FSA Research Review Vol.6(March 2010)．

Posted in Business, Finance and tagged Business Finance

This is a modified version of the report for Venture capital finance in Bath Full Time MBA Class of 2020.

Venture capital finance

Introduction

Venture capital (VC) plays a significant role for the national economy. This is primarily because although total VC investment was only less than 0.2% of GDP of the United States, VC backed firms generated 11% of all private sector jobs and earned annual revenues which was equal to 21% of GDP (Thiel, 2014). In addition, unlike general financial intermediaries such as bank finance, VC do focus on their managerial resources not only money but also expertise to certain industries including software (22% of their total investment) and biotechnology (17% of that) (Bettignies, James and Brander, 2006). This may mean that VC believe their effort and resources deeply affect the start-ups invested by them. However, it is disputed that what kind factors influence the performance of the VC backed firms. In fact, some researchers asserted that agency problems and low ability might be much less detrimental than VC backed start-ups of the dyad-partner’s sentiments of injustice, unfairness and lack of trust and therefore these feelings could be a decisive obstacle to value-creation and success in the ones. This essay will evaluate the argument in terms of venture capital theory, standard economic one and behavioral economics ones including social preferences with these evidences.

Agency problem and its influence of the start-up’s performance

According to the agency theory, there is an agency problem between the venture capitalists as a principal and the entrepreneurs as an agent who are assured fully self-interested and therefore their interest would be conflicted in a certain situation (UTSET, 2002). One of the major examples for the agency problem is adverse selection (ibid). There are good and bad entrepreneurs, however, the bad one may be able to pretend as if the good one and hence, the venture capitalists have to be able to distinguish between them (ibid). Therefore, if the venture capitalist invests in a bad entrepreneur who had low ability or even high one but low motivation, the performance of the start-up might be deteriorated. In addition, the hold-up risk is also the vital example of the agency problem. The risk is that the entrepreneur can be imperil to abandon making an effort to improve the performance of his firm invested by VC till the venture capitalist reconsiders how to divide the proportion of equity distribution (ibid). Although they can protect in the region of hold-up risk using wide range provisions, still the protection measures might be incomplete due to their inability (ibid). Moreover, the entrepreneur might behave as if their performance is better than it actually is to induce to overestimate and be invested by venture capitalist, which is called window dressing (Burchardt et al, 2016). This is also one of the most important phenomena caused by agency problems. Therefore, the entrepreneur tends to focus on the short-term performance, even if they may lose the long term one. Besides, due to the lack of ability to monitor and manage the performance, either or both of the entrepreneur and the venture capitalist may free ride others and exploit their effort, which is one of classic agency problems called free rider problem (ROMANS, 2013). Hence, the performance could be deteriorated if some of the stakeholders attempted to free ride others. Furthermore, if there is a loophole of the investment contract but the one is one of the key factor to improve higher performance, the entrepreneur’ effort in the loophole may be unobservable for VC and then the entrepreneur tend to omit the key activities in the one, which is defined as moral hazard (TUCKER, 2004). Thus, the prevention to ignore the key performance factors related activities in the contract can be important for the performance.

Dyad-partner’s sentiments and these influence of the start-up’s performance

Other factors to affect the performance are their emotions such as justice, fair and trust. Even if the venture capitalist selects a good entrepreneur who wants to manage the team, still running them is a difficult issue. For instance, some researchers argued that the perceived justice of equity distribution on entrepreneurial teams play a role for their performance (Breugst, Patzelt and Rathgeber, 2014). High perceived distributive justice causes mutual, constructive team synergy spirals, on the other hand, low one provokes unfavorable team interactions spirals and the ones further decrease perceived justice of equity distribution (ibid). This is because if their contract according to equity distribution is not perceived as fair, it seems to be that the evolution of intrateam trust is acutely damaged (ibid). In addition, it is demonstrated that as the entrepreneur feels greater fairness, VC tend to offer the equity higher and therefore, the entrepreneur might make a higher value-adding effort (Fairchild, 2010). This can be because the higher commitment to decisions, performance, behavior and attitude might be led by the increase in the perception of fairness of entrepreneurs (ibid). Furthermore, Harrison (1999 cited in TUCKER, 2004) claimed that the lack of trust between the entrepreneur and the venture capitalist may enlarge the risk which the start-up might not be lucrative. This is mainly because less able venture capitalists incline to require punitive covenants to assure themselves against the danger of inconvenience performance, which is caused by their limited ability to bring an amending control to a downside condition (ibid). Also, there is a tendency that each player prefers to distribute at least the same amount as the volume that the other players earn, which is called envy-freeness (Brams, 2005). It can be vital for the performance because if they reach envy-free distribution, no one may envy others, which means it is less likely to be the negative actions against the team. What is more, Empathy is defined as the feeling intimately linked to mutual trust between the entrepreneur and VC (Fairchild, 2009). It is suggested that the degree of the entrepreneur-VC empathy corresponding to the value-adding abilities of VC altered the entrepreneur’s selection of financier and the arising value of the VC and also argued that if the entrepreneur felt higher empathy for the VC with lower value-adding ability, the entrepreneur might select the lower ability VC rather than higher one and hence the performance of the firm would be decreased (ibid). This may mean that the performance of the empathically biased entrepreneur tends to be lower than the performance of the unbiased one. Additionally, it is asserted that if the entrepreneur has the overconfidence and unrealistic optimism, they may ignore some important figures and signs which is against their buoyant forecast and therefore they might serve to induce their miscalculation of the possibility of new venture failure linked to the potential investors of their company control who are less overconfident (Douglas, Carlsson-Wall and Hjelström, 2014). This is because although the probability of the company that consequently fail might be calculated as an objective measure of the default probability if they are in high competitive market, if the entrepreneur and their firm having a new service enter to a new market which has a few competitors or no completion, the probability of failure must be estimated subjectively based on their unrealistic point of view and unfeasible forecast (ibid). Hence, the overconfidence of the entrepreneur might deteriorate the performance of the start-ups due to unfeasible forecasts induced by their overconfidence. Correspondingly, some researchers indicated that the over-optimistic entrepreneurs interpret transactional facts hypothetically that understates consequent risks, which they fail to invest in collecting transactional-specific information and tend to enter transactions without consultation of the external advisors. (UTSET, 2002). Therefore, over-optimism may induce an entrepreneur to participate in the contracts which do not count on the actual risks that the start-ups may suffer (ibid). Even if the over-optimistic entrepreneur completely comprehends the arduous arrangements in a venture capital contract, they would not be certainly concerned, assuming such events which would cause these adverse agreements will not be realized (ibid). However, during the cycle of the start-up, when unfavorable cases of the planet induce demanding provisions in VC contracts, the initial over-optimistic expectations of the entrepreneur will introduce blunt facts relative to the real nature of the proper conditions (ibid). Thus, the over-optimism of the entrepreneur might affect their performance due to unfeasible contracts agreed with VC. This is because they may not prepare unpreferable situations which are likely to happen. Finally, looking at negative feelings, such sentiment may lead to revenge for the company and then the performance of the one could be declined (UTSET, 2002). This is because the angered player such as an employee might be ready to commit in active sabotage or to deliver indirect actions including not employing enough effort, even if the explicit profits of doing so seem to be less than the expenses (ibid).

Comparison between standard economic and behavioral theory

One of the feasible tools to analyze the economic and social situation is game theory. For instance, as a result of game theory which is assured the players are fully rational, they might reach the equilibrium to avoid the conflictions mainly caused by the agency problem above such as adverse selection, hold-up risk, window dressing, free rider problem and moral hazard (Fairchild and Yao, 2017). The equilibrium might say that all rational venture capitalists ought to fairly suggest 43% of the equity to the entrepreneur, holding 57% themselves, and all of the players in the dyad should exert their power (ibid). On the other hand, after counting on the emotion of the entrepreneur and the venture capitalist such as fairness, empathy and engagement among the duo, the equilibrium is moved and then reached a new one which is relatively balanced (almost 50/50) (ibid). This can mean in general, the venture capitalists may be superior to the entrepreneurs mainly due to their expertise, such advantage might not affect to improve performance in the long run because of their sentiments and therefore, both of them can consider this emotional effect to the equity distribution.

Conclusion

This essay has assessed the argument that a crucial barrier to value-creation and success in VC backed prospective start-ups is that of the dyad-partners’ sentiments which can be furthermore detrimental than agency problems and low ability. To this end, it has discussed the effects of agency problems and Dyad-partner’s sentiments for the performance, and also the comparison between standard economic and behavioral theory relative to both aspects. It is concluded that agency problems might induce mainly moral hazard, hold-up risk, free-riding and window dressing, which could decline the performance. Also, Dyad-partner’s sentiments are primary injustice, unfairness. lack of trust, envy, empathy, overconfident and negative reciprocity (revenge), which might deteriorate the performance and therefore emotionally biased the entrepreneur tend to be lower performer than unbiased one. In addition, the major difference between standard economic and behavioral theory can be typically observed in the equilibrium of the equity distribution in dyad partners. The emotion of the entrepreneur might require more equal amount of the equity even if they recognize asymmetry information with VC and thus the difference might be the premium for any type of counter actions against unfairness.

Reference

  • Bettignies, J.D., James A. and Brander, J.A., 2006. Financing entrepreneurship: Bank finance versus venture capital
  • Brams, S.J., 2005. Fair Division
  • Breugst, N., Patzelt, H. and Rathgeber, P., 2014. How should we divide the pie? Equity distribution and its impact on entrepreneurial teams
  • Burchardt, J., Hommel, U., Kamuriwo, D. S. & Billitteri, C., 2016. Venture capital contracting in theory and practice: Implications for entrepreneurship research. Entrepreneurship: Theory and Practice, 40(1), pp. 25-48. doi: 10.1111/etap.12104
  • Douglas, E.J., Carlsson-Wall, M. and Hjelström, T., 2014. Negotiating equity share and management control of the entrepreneurial new venture, Venture Capital, 16:4, 287-307, DOI: 10.1080/13691066.2014.970334
  • Fairchild, R. and Yao, Y., 2017. Venture Capital/Entrepreneurial contracting and performance: An Experimental Investigation
  • Fairchild, R., 2009. An entrepreneur’s choice of venture capitalist or angel-financing: A behavioral game-theoretic approach
  • Fairchild, R., 2010. Fairness Norms and Self-interest in Venture Capital/Entrepreneur Contracting and Performance
  • ROMANS, A., 2013. THE ENTREPRENEURIAL BIBLE TO VENTURE CAPITAL
  • Thiel, P., 2014, Zero to One
  • TUCKER, J.A., 2004. LEVERAGING THE VENTURE CAPITAL RELATIONSHIP – THE ENTREPRENEURS’ PERSPECTIVE
  • UTSET, M.A., 2002. RECIPROCAL FAIRNESS, STRATEGIC BEHAVIOR & VENTURE SURVIVAL: A THEORY OF VENTURE CAPITAL- FINANCED FIRMS

Posted in Business, Finance, Marketing and tagged Business Finance Marketing

This is a modified version of the report for Strategic brand management in Bath Full Time MBA Class of 2020.

Strategic brand management

Introduction

In-store purchasing process can be one of the most significant parts among all kinds of processes including online. This is primary because retail market is the largest industry in the all category of the industries such as automobile and it still keeps to grow the sales, for example, the revenue of the world largest retailer (WalMart) doubles in size every five years, which is more than 2 times larger than Amazon (the top online retailer in the world). In fact, only one square meter of sales space can earn 80.000.000 US dollars per year. Therefore, the retailers still are vitally important as a major channel and therefore the research of that is advancing rapidly. On the other hand, an online retailer is building its physical one and vice versa then ‘online merge offline’ might be going faster. To combine in-store marketing with online one, this essay will discuss how to build the brand online to use the online trading platform as an example.

##Future Work For the purpose of this essay, it is considered how to build a brand for selling a certain product via landing page on the web. More specifically, the product assumed the commission-free investing online platform which can be the alternative of Robinhood. The user can invest in most financial products such as stocks and forex after creating their account without no or a few commissions.

Segmentation, Targeting and Positioning

In addition, from the marketing viewpoint, it should be focused on a specific customer segment. Generation C can be consistent with the purpose as a target customer. This is primary because they have two main features which are young (born between 1982 and 1996) and tech-savvy that means they relate to each other via social media such as YouTube and Facebook (PICKETT, 2019).

Four Es as an Alternative Marketing mix 4 Ps

4 Ps stand for product, price, place and promotion, on the other hand, 4 Es do so experience, exchange, everywhere and evangelism (Poulou, 2018). This is due to the customers wanting a certain experience from the service, rather than just consuming the product (ibid). In addition, some contemporary businesses provide its service for them without any charges and then instead of the fee, it sells the data of them and advertising space (ibid). Furthermore, most customers connect to the Internet mainly via mobile phone and therefore, they can buy the product everywhere (ibid). Moreover, although traditional advertising such as TV commercials is still important, customer evangelists are also becoming a significant factor to sell the products due to the huge social media networks (ibid). Therefore, it is primary important to consider how to advertise the product via influencers. For instance, the young famous venture capitalists and investors can play the key role for the product advertising in this essay and operation costs can be compensated by sales of data instead of commission.

Two Systems of Thinking

It is also important to analyze how the customer, especially the target one, thinks about the product. According to Kahneman (2012), people have two different systems of thinking processes which are called system 1 and system 2. Former administers automatically and immediately with little or no effort and no space to be worked by voluntary control (ibid). The latter, on the other hand, assigns attention to the arduous mental activities which require it such as complicated computations (ibid). Hence, the purchasing process can be mainly related to unconscious thinking. It is supported by the fact that its brand can have the biggest influence in the purchasing decision primary because in certain type of products, for example, top 10 brands of beer dominated more than 70 % of total share of the United States beer sales in 2002 (Corstjens and Steele, 2008). It can be also supported by the eye tracking observations. This is because the subjects of the eye tracking experiment seems to have quite narrow eye sight which only focus on the middle and low of goods shelves and their decision making tend to be relatively quick (a few second), which may mean they decide to buy the goods unconsciously based on the limited information such as price and brand (Nordfält, 2020).

Customer Decision Journey

One of the best methods to monitor the progress can be retention rate to purchase a target product (or service). This is mainly because the first trial of the product could be driven by the marketing and sales activities such as discounting and up (cross) selling, not purely the intrinsic value of the one and therefore, the purchase after trial can be expected to mitigate the effect of sales and marketing. The decision process journey can be divided to the four cycles which are initial consideration, active evaluation, closure and post purchase (Court et al., 2009). In the post purchase, it is assumed that the customer builds the expectation of the bought product and hence they will decide if they repurchase the one, which is called ‘loyalty loop’ (ibid). Thus, retention rate might be estimated to monitor loyalty loop . Hence, the brand discussed in this essay should be to strengthen the loyalty loop which can be monitored by retention rate, which means the brand can be said to be associated with a product category (for instance, an online investment platform) when the customer purchases the service in brands.

Brand Association Map

In fact, a brand association map is a strategic, comprehensive framework which can provide the implication its brand has vis‐à‐vis main competitors (Till, Baack and Waterman, 2011). The maps describe a brand and its associations besides an evaluation of the strength, relevance, uniqueness and favorability of each association (ibid). In addition, a strong brand has stronger and more intensive association (strength and relevance), larger positive futures (favorability) and sharper distinct futures within the product category (uniqueness). The map can be built by the customer experience (CX) including pre and post purchase one. Therefore, sales and marketing strategy of the product should be focused on increasing the four points (strength, relevance, uniqueness and favorability). One of the major examples of increasing its brand value can be HSBC, the board of which developed its audited brand value from nearly zero in 1999 to $10 billion in 2005 to send the customers the message which is ‘the world’s local bank’ (Beverland, 2018). In fact, its logo (hexagon) can be associated with banks and icons in advertising shows the respect for cultural difference. For example, the symbol of tea in China is different from Turkey (ibid). Therefore, the landing page of the product in this essay, especially its design should be changed by the visitor’s attributions.

Search Engine Optimization

The customer can buy the product everywhere, however, the entrance of the Internet seems to be dominated by only a few search engines such as Google and YouTube. Hence, it is inevitable to find how to optimize the engines, one of the most fundamental strategies of which can be maximize the number of links. This is mainly because there is a stable relationship in correlation between links and ranking from 2007 to 2020 and high correlation between authoritative links and ranking (Nordfält, 2020). Thus, the landing page of the product in this essay needs the links to be searched by the target customers.

Conclusion

This essay has discussed how to build the brand on the web using the online trading platform as an example. The target segment decided Gen C and then the evangelists did so young VCs and investors. The logo of the product should be a simple and single icon, however, advertising for it and the landing page should be varied by customer attributions. Also, the landing page should optimize the search engines to increase the number of the links. Finally, these experiments should be monitored by the retention rate which is the equivalent of a loyalty loop in the customer decision journey.

Reference