Equity markets are amongst the most researched areas in asset pricing literature. Data availability and the liquid and transparent nature of equity markets have aided research in this domain. The research on corporate bond markets is considerably less due to both the illiquid and over-the-counter (OTC) nature of these markets which have resulted in less easy availability of reliable data sources. Corporate bond and equities possess commonalities in their behaviour largely because of being at different points in the capital structure of firms. Indeed, adverse news for a company should adversely affect the pricing of both the firm’s equity and debt. As a result, practitioners often consider corporate bonds as a combination of government-bonds and beta-adjusted equities used as a proxy for credit exposure. In the thesis however, we seek to demonstrate that credit risk, although highly correlated in the short term, can be different from equity risk. The seminal work on the pricing of corporate debt was by Robert Merton (Merton 1974). The Merton model represented corporate debt as the combination of a risk-free asset and a short position in a put option on the assets of the firm. Equity was represented as a long call option on the assets of the firm. Since then models such as Black and Cox (1976) and Leland (1994) have extended the Merton model but the key features of corporate bond pricing and its co-movement with equity prices are still well represented by the Merton model. The Merton model, while capturing a point of commonality – the common effect of changes in asset prices to equity and debt price – and a key difference – the left-tailed nature of corporate debt returns – does not address other key areas of differences between the two asset classes. One area of difference, studied extensively in the empirical literature, but not in structural models is the significant difference in liquidity and trading dynamics between the two markets. Another key area of difference between the two markets comes from the differing type of investors. Regulations, which are much more onerous for corporate debt than equities, can lead to non-market-driven behaviour such as a significant aversion to downgrades. The goal of my PhD thesis is to study the commonality and differences between these two asset classes and Its implication on the cross-section of corporate bond returns. Specifically, we look at three aspects of differences between corporate and equities. The first chapter focuses on the issuance of corporate bonds and contrasts with equity issuance. It starts with the issuance process and analyses the new issue premiums in corporate bonds contrasting it with results seen in equity initial public offerings (IPOs). This chapter also analyses the determinants of corporate bond issuance concessions. The second chapter looks at the short-term commonalities and differences between the performance patterns of corporate bonds and equities. This chapter merges two distinct branches of literature on structural credit models and commonalities in corporate bond-equity behaviour with that of cross-asset momentum. The last two chapters focus on the topical area of exchange traded funds and their dislocations, as measured by the significant deviations between prices and net-asset-values (NAV), seen in this market during the extreme volatility at the peak of the Covid-19 crisis in March 2020. Specifically in chapter 4, we study the dislocation in fixed-income and specifically corporate bond ETFs and contrast it with the relatively better-behaved equity ETFs. We show that this relative dislocation is not just from liquidity differences and that the ETF price may have been an over-reaction. In chapter 5, we build a model for ETF arbitrage specifically taking into account incentives of the arbitrageurs, a critical difference between fixed income and equity ETFs. We show that inventory management by dual market makers and arbitrageurs may have exacerbated the dislocation.