TIMELY INFORMATION INSIDE

Convertible and High Income Fund (CHY)

SEMIANNUAL REPORT APRIL 30, 2018

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TABLE OF CONTENTS

Letter to Shareholders1

The Calamos Closed-End Funds:
An Overview5

Investment Team Discussion6

Schedule of Investments10

Statement of Assets and Liabilities26

Statement of Operations27

Statements of Changes In Net Assets28

Statement of Cash Flows29

Notes to Financial Statements30

Financial Highlights38

Report of Independent Registered
Public Accounting Firm39

About Closed-End Funds40

Managed Distribution Policy41

Automatic Dividend Reinvestment Plan41

Experience and Foresight

About Calamos Investments

For over 40 years, we have helped investors like you manage and build wealth to meet their long-term individual objectives by working to capitalize on the opportunities of the evolving global marketplace. We launched our first mutual fund in 1985 and our first closed-end fund in 2002. Today, we manage six closed-end funds. Three are total-return oriented offerings, which seek current income, with increased emphasis on capital gains potential. Three are enhanced fixed income offerings, which pursue high current income from income and capital gains. Calamos Convertible and High Income Fund (CHY) falls into this latter category. Please see page 5 for a more detailed overview of our closed-end offerings.

We are dedicated to helping our clients build and protect wealth. We understand when you entrust us with your assets, you also entrust us with your achievements, goals and aspirations. We believe we best honor this trust by making investment decisions guided by integrity, by discipline, and by our conscientious research.

We believe an active, risk-conscious approach is essential for wealth creation. In the 1970s, we pioneered strategies that seek to participate in equity market upside and mitigate some of the potential risks of equity market volatility. Our investment process seeks to manage risk at multiple levels and draws upon our experience investing through multiple market cycles.

We have a global perspective. We believe globalization offers tremendous opportunities for countries and companies all over the world. In our view, this creates significant opportunities for investors. In our U.S., global and international portfolios, we are seeking to capitalize on the potential growth of the global economy.

We believe there are opportunities in all markets. Our history traces back to the 1970s, a period of significant volatility and economic concerns. We have invested through multiple market cycles, each with its own challenges. Out of this experience comes our belief that the flipside of volatility is opportunity.

John P. calamos, sr.

Founder, Chairman
and Global Chief
Investment Officer

CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT   1

Dear Fellow Shareholder:

Welcome to your semiannual report for the six-month period ended April 30, 2018. In this report, you will find commentary from the Calamos portfolio management team, as well as a listing of portfolio holdings, financial statements and highlights, and detailed information about the performance and positioning of this Calamos Fund. I encourage you to review this information carefully.

Calamos Convertible and High Income Fund (CHY) is an enhanced fixed income fund. We utilize dynamic asset allocation to pursue high current income with a less rate sensitive approach, while also maintaining a focus on capital gains. We believe the flexibility to invest in high yield corporate bonds and convertible securities is an important differentiator, especially given political as well as fiscal and monetary policy unknowns, and their potential impact on interest rates and the fixed income market.

Distribution

During the period, the Fund provided a compelling monthly distribution of $0.1000 per share. We believe the Fund’s current annualized distribution rate, which was 9.90%* on a market price basis as of April 30, 2018, was very competitive, given the low interest rates in many segments of the bond market. In our view, the Fund’s distributions illustrate the benefits of a multi-asset class approach and flexible allocation strategy.

We understand that many closed-end fund investors seek steady, predictable distributions instead of distributions that fluctuate. Therefore, this Fund has a managed distribution policy. As part of this policy, we aim to keep distributions consistent from month to month, and at a level that we believe can be sustained over the long term. In setting the Fund’s distribution rate, the investment management team and the Fund’s Board of Trustees consider the interest rate, market and economic environment. We also factor in our assessment of individual securities and asset classes.

*Current Annualized Distribution Rate is the Fund’s most recent distribution, expressed as an annualized percentage of the Fund’s current market price per share. The Fund’s 4/30/18 distribution was $0.1000 per share. Based on our current estimates, we anticipate that approximately $0.1000 is paid from ordinary income or capital gains and that approximately $0.0000 represents a return of capital. Estimates are calculated on a tax basis rather than on a generally accepted accounting principles (GAAP) basis, but should not be used for tax reporting purposes. Distributions are subject to re-characterization for tax purposes after the end of the fiscal year. This information is not legal or tax advice. Consult a professional regarding your specific legal or tax matters. Under the Fund’s managed distribution policy, distributions paid to common shareholders may include net investment income, net realized short-term capital gains and return of capital. When the net investment income and net realized short-term capital gains are not sufficient, a portion of the distribution will be a return of capital. In addition, a limited number of distributions per calendar year may include net realized long-term capital gains. The distribution rate may vary.

2   CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT

In our October 2017 annual report, I discussed the favorable trends that were supporting continued global growth and investment potential across asset classes. However, I noted our investment teams would not be surprised if the market environment changed, with a pause in the equity markets or even a correction. I also discussed that short-term volatility can create opportunities for long-term managers, such as ourselves. During the semiannual reporting period, these views were borne out.

Market Review

The semiannual period was characterized by two distinct environments, and in particular, the return of volatility to the markets in January. Through the final months of 2017, U.S. and global stock markets advanced briskly as investors focused on positive global economic growth trends, low inflation, deregulation and anticipation of tax reform. However, the climate changed in 2018. Although economic fundamentals remained compelling around the world, market participants became distracted by the potential for more Federal Reserve hikes and rising inflation. After many years of subdued volatility and record-low interest rates, the stock market became increasingly turbulent as the period progressed.¹ Fixed income asset classes also encountered headwinds.^2,3 Convertible securities, in contrast, demonstrated resilience in the choppy markets, illustrating the potential benefits of their unique structural characteristics.⁴

Outlook

We believe positive economic conditions and corporate fundamentals can support a continuation of the bull market in stocks, as well as opportunities across asset classes. Global economic data is positive on the whole. GDP growth has continued at a good pace in the U.S., and tax reform and deregulation can provide further catalysts from here. The U.S. consumer has benefitted from job growth, wage gains and rising housing values. Corporate fundamentals—including earnings, sales and revenue growth—are very strong. Inflation has increased but is coming off historically low levels and remains contained. As economic growth continues, we expect the Fed to maintain its course of raising short-term interest rates gradually. This slow pace, combined with conditions in the broader global bond markets, may help keep longer-term U.S. rates from rising unchecked.

Although economic conditions are favorable, managing volatility will be key to succeeding in this environment. Evolving trade policies, uncertainties around North Korea and Russia, and U.S. mid-term elections will likely contribute to short-term market disruptions over coming months. An extended trade war could be an economic headwind, but we do not see this as the probable outcome. We are hopeful that moves by the U.S. over recent months can set the stage for negotiations that lead to freer and fairer trade over the long term.

CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT   3

Thoughts for Investors

The stock market’s gyrations, rising interest rates and signs of inflation have unsettled many investors. However, if we look back over longer periods, the environment we are seeing today is actually more normal than those of the past few years when volatility, interest rates and inflation were exceptionally low.

In this more typical environment, we believe there are many opportunities for active and risk-aware approaches. Our investment professionals remain vigilant to avoiding unintended risks in the Fund. They are also working together to turn short-term volatility into opportunities for the shareholders in the Fund. Our ability to respond to changing market conditions will be especially important given the many crosscurrents we see.

In Closing

More than 40 years of experience supports my belief that investors are best served by maintaining a long-term approach. Fast moving markets can increase the temptation to make short-term moves. But as I’ve noted in the past, there’s no way to predict with certainty the daily twists and turns. Far too often, trying to time the ups and downs leaves investors capturing the downside and missing the upside. Instead, I encourage you to work with your financial advisor to create a well-diversified asset allocation that meets your financial goals. By blending an array of funds—including stocks, convertibles, alternative and fixed income strategies—investors may be better positioned to achieve their long-term goals.

I am confident that the Fund is well equipped to navigate the course ahead. Since our earliest days as an asset manager, we have sought to provide innovative strategies for managing risk and enhancing returns. While others may be discouraged by these more choppy markets, we welcome the return of more normal levels of volatility and the opportunities it will bring for our active approach.

I hope that you find this report informative, and I invite you to visit our website www.calamos.com for additional resources. All of us at Calamos Investments thank you for your continued trust. It is truly an honor to help you achieve your financial goals.

Sincerely,

John P. Calamos, Sr.

Founder, Chairman and Global Chief Investment Officer

4   CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT

Before investing, carefully consider a fund’s investment objectives, risks, charges and expenses. Please see the prospectus containing this and other information or call 800.582.6959. Please read the prospectus carefully. Performance data represents past performance, which is no guarantee of future results. Current performance may be lower or higher than the performance quoted. Opinions are as of the publication date, subject to change and may not come to pass. Information is for informational purposes only and shouldn’t be considered investment advice.

¹The MSCI All Country World Index is a measure of global stock market performance, which returned 3.83% for the six-month period ending April 30, 2018. The MSCI World Index is a market-capitalization weighted index composed of companies representative of the market structure of developed market countries in North America, Europe and the Asia/Pacific region. For the six-month period ended, the index returned 3.68%. The S&P 500 Index is an unmanaged index generally considered representative of the U.S. stock market. For the six-month period, the index returned 3.82%. The MSCI Emerging Markets Index is a free float-adjusted market capitalization index considered broadly representative of emerging market equity performance. The index represents companies within the constituent emerging markets that are available to investors worldwide, and it returned 4.93% for the six-month period ended April 30, 2018.

²The Bloomberg Barclays U.S. Aggregate Bond Index is considered generally representative of the investment-grade bond market. For the six-month period ending April 30, 2018, the index returned -1.87%.

³The Credit Suisse U.S. High Yield Index is an unmanaged index of high yield debt securities, which returned -0.16% for the six-month period ending April 30, 2018.

⁴The ICE BofAML All U.S. Convertibles ex-Mandatory Index represents the U.S. convertible securities market excluding mandatory convertibles. The index returned 2.34% for the six-month period ending April 30, 2018. The ICE BofAML Global 300 Convertible Index is a global convertible index composed of companies representative of the market structure of countries in North America, Europe and the Asia/Pacific region. The index returned 3.95% for the six-month period ended April 30, 2018.

Sources: Lipper, Inc.

Unmanaged index returns assume reinvestment of any and all distributions and, unlike fund returns, do not reflect fees, expenses or sales charges. Investors cannot invest directly in an index. Investments in overseas markets pose special risks, including currency fluctuation and political risks. These risks are generally intensified for investments in emerging markets. Countries, regions, and sectors mentioned are presented to illustrate countries, regions, and sectors in which a fund may invest. Fund holdings are subject to change daily. The Funds are actively managed.

The information contained herein is based on internal research derived from various sources and does not purport to be statements of all material facts relating to the securities mentioned. The information contained herein, while not guaranteed as to accuracy or completeness, has been obtained from sources we believe to be reliable. There are certain risks involved with investing in convertible securities in addition to market risk, such as call risk, dividend risk, liquidity risk and default risk, that should be carefully considered prior to investing. This information is being provided for informational purposes only and should not be considered investment advice or an offer to buy or sell any security in the portfolio. Investments in alternative strategies may not be suitable for all investors.

This report is intended for informational purposes only and should not be considered investment advice.

CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT   5

In our closed-end funds, we draw upon decades of investment experience, including a long history of opportunistically blending asset classes in an attempt to capture upside potential while seeking to manage downside risk. We launched our first closed-end fund in 2002.

Closed-end funds are long-term investments. Most focus on providing monthly distributions, but there are important differences among individual closed-end funds. Calamos closed-end funds can be grouped into multiple categories that seek to produce income while offering exposure to various asset classes and sectors.

Our Managed Distribution Policy

Closed-end fund investors often seek a steady stream of income. Recognizing this important need, Calamos closed-end funds adhere to a managed distribution policy in which we aim to provide consistent monthly distributions through the disbursement of the following:

•Net investment income

•Net realized short-term capital gains

•Net realized long-term capital gains

•And, if necessary, return of capital

We set distributions at levels that we believe are sustainable for the long term. Our team focuses on delivering an attractive monthly distribution, while maintaining a long-term emphasis on risk management. The level of the funds’ distributions can be greatly influenced by market conditions, including the interest rate environment, the individual performance of securities held by the funds, our view of retaining leverage, fund tax considerations, and regulatory requirements.

You should not draw any conclusions about the Fund’s investment performance from the amount of this distribution or from the terms of the Fund’s plan. The Fund’s Board of Trustees may amend or terminate the managed distribution policy at any time without prior notice to the Fund’s shareholders.

For more information about any Calamos closed-end funds, we encourage you to contact your financial advisor or Calamos Investments at 800.582.6959 (Monday through Friday from 8:00 a.m. to 6:00 p.m., Central Time). You can also visit us at www.calamos.com.

6   CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT

TOTAL RETURN* AS OF 4/30/18

SECTOR WEIGHTINGS

Sector Weightings are based on managed assets and may vary over time. Sector Weightings exclude any government/sovereign bonds or options on broad market indexes the Fund may hold.

CONVERTIBLE AND HIGH INCOME FUND (CHY)

INVESTMENT TEAM DISCUSSION

Please discuss the Fund’s strategy and role within an asset allocation framework.

Calamos Convertible and High Income Fund (CHY) is an enhanced fixed income offering that seeks total return through a combination of capital appreciation and current income. It provides an alternative to funds investing exclusively in investment-grade fixed income instruments and seeks to be less sensitive to interest rates. Like all Calamos closed-end funds, the Fund seeks to provide a steady stream of distributions paid out monthly and invests in multiple asset classes, which can be reweighted in an effort to optimize returns.

We invest in a diversified portfolio of convertible securities and high yield securities. The allocation to each asset class is dynamic and reflects our view of the economic landscape as well as the potential of individual securities. By combining these asset classes, we believe that the Fund is well positioned to generate capital gains and income. We believe the broader range of security types also provides increased opportunities to manage the risk/reward characteristics of the portfolio over full market cycles. During the six-month period, ended April 30, 2018, the Fund maintained a high proportional exposure to convertible assets. We believe such exposure, which constituted over half the portfolio at the end of the period, positions us well to participate in the equity markets in a more risk-managed way in 2018.

We seek companies with respectable balance sheets, reliable debt servicing and good prospects for sustainable growth. While we invest primarily in securities of U.S. issuers, we favor companies that are actively participating in globalization with geographically diversified revenue streams and global-scale business strategies.

How did the Fund perform over the reporting period?

The Fund returned 1.35% on a net asset value (NAV) basis and 6.63% on a market price basis for the six-month period ended April 30, 2018 versus the -0.16% Credit Suisse U.S. High Yield Index and 2.11% increase for the ICE BofAML All U.S. Convertibles Index.

At the end of the reporting period, the Fund’s shares traded at a 5.21% premium to net asset value.

CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT   7

SINCE INCEPTION MARKET PRICE AND NAV HISTORY THROUGH 4/30/18

Performance data quoted represents past performance, which is no guarantee of future results. Current performance may be lower or higher than the performance quoted. The principal value of an investment will fluctuate so that your shares, when sold, may be worth more or less than their original cost. Returns at NAV reflect the deduction of the Fund’s management fee, debt leverage costs and all other applicable fees and expenses. You can obtain performance data current to the most recent month end by visiting www.calamos.com.

How do NAV and market price return differ?

Closed-end funds trade on exchanges, where the price of shares may be driven by factors other than the value of the underlying securities. The price of a share in the market is called market value. Market price may be influenced by factors unrelated to the performance of the fund’s holdings, such as general market sentiment or future expectation. A fund’s NAV return measures the actual return of the individual securities in the portfolio, less fund expenses. It also measures how a manager was able to capitalize on market opportunities. Because we believe closed-end funds are best utilized long term within asset allocations, we believe that NAV return is the better measure of a fund’s performance. However, when managing the fund, we strongly consider actions and policies that we believe will optimize its overall price performance and returns based on market value.

Please discuss the Fund’s distributions during the six-month period.

We employ a managed distribution policy* within this Fund with the goal of providing shareholders a consistent distribution stream. In each month of the period, the Fund distributed $0.1000 per share, resulting in a current annualized distribution rate of 9.90% of market price as of April, 30, 2018.

We believe that both the Fund’s distribution rate and level remained attractive and competitive, as low interest rates limited yield opportunities in much of the marketplace. For example, as of April 30, 2018, the dividend yield of S&P 500 Index stocks averaged approximately 2.11%.† Yields also were still relatively low within the U.S. government bond market, with the 10-year U.S. Treasury and 30-year U.S. Treasury yielding 2.95% and 3.11%, respectively.‡

*Under the Fund’s managed distribution policy, distributions paid to common shareholders may include net investment income, net realized short-term capital gains and return of capital. When the net investment income and net realized short-term capital gains are not sufficient, a portion of the distribution will be a return of capital. In addition, a limited number of distributions per calendar year may include net realized long-term capital gains. The distribution rate may vary.

†Source: Calamos Investments

‡Source: U.S. Department of the Treasury

8   CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT

What factors influenced performance over the reporting period?

Improvements in the convertible bond markets contributed to the Fund’s positive performance over the period. Convertible bond Issuance was also robust during the period, which presented us with a broad selection of investment opportunities.

The Fund’s attractive share price relative to the NAV earlier in the period served as an enticement to many investors and enhanced price performance.

From an economic sector perspective, selection in healthcare (biotechnology) contributed to performance. In addition, the Fund was helped by its underweight to real estate, notably in diversified REITs.

Our selection in materials (steel) hindered performance. In addition, our names in consumer discretionary (internet and direct marketing retail) lagged relative to the ICE BofAML All U.S. Convertibles Index.

How is the Fund positioned?

We continue to hold our highest allocation of rated securities in the BB-credit tier, as we believe this exposure offers investors a better risk/reward dynamic while continuing to provide regular income. From an economic sector perspective, our heaviest exposures are found in the information technology, health care and consumer discretionary sectors. We believe that these sectors should outperform given where we are in the economic cycle and based on current demographic trends. We continue to maintain significant positions in convertible securities, which we believe can provide income, benefit from a rising equity market, and manage overall portfolio risk. As of April 30, 2018, approximately 55% our portfolio was invested in convertible securities. We believe this will enable our shareholders to take advantage of opportunities in the general equity markets. Long term, we believe patient investors will be rewarded for an allocation to convertibles and high yield at current levels, especially during periods of market volatility.

The average credit quality of the portfolio is slightly higher than that of the ICE BofAML All U.S. Convertibles Index. This is typical for the Fund, as our credit process tends to guide us away from the most speculative corporate securities. That said, we do selectively invest in lower-credit securities when we believe the risk/reward dynamics are favorable for our investors.

Moreover, we seek to invest where the risk/reward is compelling, investing in global businesses who have diversified their revenue streams by capitalizing on the best opportunities around the world. Overall, we believe that our portfolio companies are performing well fundamentally and are well positioned to participate in global synchronization, earn attractive cash flow margins, and improve their credit profiles while utilizing reasonable debt levels to fund their operations.

We believe that this is an environment that is conducive to the prudent use of leverage as a means of enhancing total return and supporting the fund’s distribution rate. In spite of a cost increase due to rising interest rates, our use of leverage over the period enjoyed a favorable reinvestment dynamic.

CALAMOS Convertible and High Income Fund SEMIANNUAL REPORT   9

What are your closing thoughts for Fund shareholders?

Given our outlook for a continued period of economic growth, we are favoring quality growth companies. Favorable factors within the U.S. include solid job creation, low interest rates, improved consumer spending and limited inflationary pressures. We emphasize investments in companies with solid cash flow generation and stronger balance sheets. From a thematic and sector perspective, we see opportunities in the technology sector, consumer discretionary companies tied to global consumption, and companies positioned to benefit from improving fundamentals. We are also optimistic about financials, as we believe financial companies are favorably valued and positioned to grow revenues in a rising-interest-rate, lower-regulatory environment. We are cautious about companies in the consumer staples sector. We believe they may be fully valued as investors are attracted to those stocks for income rather than growth. We are selective regarding companies in the healthcare sector, favoring those that are more product-growth oriented versus price driven.

We believe that fiscal policy is likely to remain an important factor regarding the impact of rate hikes on corporate refinancing of debt. In addition, geopolitical concerns will likely be an ongoing consideration. In our view, equities continue to offer compelling risk/reward potential.

Investing in convertibles provides a means to participate in a portion of the equity market upside and to achieve a degree of downside protection. We expect markets to have bouts of turbulence, which we see as a positive for convertibles. In this respect, we believe returns are best viewed over a full market cycle. We are focused on the more balanced convertibles,** which we believe can be beneficial in a volatile market as they are more likely to limit losses in down markets and participate in up markets. We are also encouraged by the continued issuance of new convertibles, which should provide broad investment opportunities through the space. Our dynamic allocation mandate allows us to deploy assets across different asset classes to benefit our shareholders. Accordingly, we believe that active management in the convertible and high yield asset classes is essential to achieving desirable risk-managed results over time, especially during periods of market volatility.

**Balanced convertibles display an asymmetric upside/downside risk profile versus the common stock that they convert into. This means they generally show less downside risk relative to their underlying stocks and participate in a greater portion of the underlying stock’s upside than downside.